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Showing 1 - 16 of 16 matches in All departments

Free Resolutions in Commutative Algebra and Algebraic Geometry (Hardcover): David Eisenbud Free Resolutions in Commutative Algebra and Algebraic Geometry (Hardcover)
David Eisenbud
R3,805 Discovery Miles 38 050 Ships in 12 - 17 working days

The selected contributions in this volume originated at the Sundance conference, which was devoted to discussions of current work in the area of free resolutions. The papers include new research, not otherwise published, and expositions that develop current problems likely to influence future developments in the field.

3264 and All That - A Second Course in Algebraic Geometry (Hardcover): David Eisenbud, Joe Harris 3264 and All That - A Second Course in Algebraic Geometry (Hardcover)
David Eisenbud, Joe Harris
R2,135 Discovery Miles 21 350 Ships in 12 - 17 working days

This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles' nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincare's development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics.

Commutative Algebra and Noncommutative Algebraic Geometry: Volume 2, Research Articles (Hardcover): David Eisenbud, Srikanth B.... Commutative Algebra and Noncommutative Algebraic Geometry: Volume 2, Research Articles (Hardcover)
David Eisenbud, Srikanth B. Iyengar, Anurag K. Singh, J. Toby Stafford, Michel Van den Bergh
R2,346 Discovery Miles 23 460 Ships in 12 - 17 working days

In the 2012-13 academic year, the Mathematical Sciences Research Institute, Berkeley, hosted programs in Commutative Algebra (Fall 2012 and Spring 2013) and Noncommutative Algebraic Geometry and Representation Theory (Spring 2013). There have been many significant developments in these fields in recent years; what is more, the boundary between them has become increasingly blurred. This was apparent during the MSRI program, where there were a number of joint seminars on subjects of common interest: birational geometry, D-modules, invariant theory, matrix factorizations, noncommutative resolutions, singularity categories, support varieties, and tilting theory, to name a few. These volumes reflect the lively interaction between the subjects witnessed at MSRI. The Introductory Workshops and Connections for Women Workshops for the two programs included lecture series by experts in the field. The volumes include a number of survey articles based on these lectures, along with expository articles and research papers by participants of the programs. Volume 2 focuses on the most recent research.

Commutative Algebra and Noncommutative Algebraic Geometry: Volume 1, Expository Articles (Hardcover): David Eisenbud, Srikanth... Commutative Algebra and Noncommutative Algebraic Geometry: Volume 1, Expository Articles (Hardcover)
David Eisenbud, Srikanth B. Iyengar, Anurag K. Singh, J. Toby Stafford, Michel Van den Bergh
R2,955 Discovery Miles 29 550 Ships in 12 - 17 working days

In the 2012-13 academic year, the Mathematical Sciences Research Institute, Berkeley, hosted programs in Commutative Algebra (Fall 2012 and Spring 2013) and Noncommutative Algebraic Geometry and Representation Theory (Spring 2013). There have been many significant developments in these fields in recent years; what is more, the boundary between them has become increasingly blurred. This was apparent during the MSRI program, where there were a number of joint seminars on subjects of common interest: birational geometry, D-modules, invariant theory, matrix factorizations, noncommutative resolutions, singularity categories, support varieties, and tilting theory, to name a few. These volumes reflect the lively interaction between the subjects witnessed at MSRI. The Introductory Workshops and Connections for Women Workshops for the two programs included lecture series by experts in the field. The volumes include a number of survey articles based on these lectures, along with expository articles and research papers by participants of the programs. Volume 1 contains expository papers ideal for those entering the field.

Minimal Free Resolutions over Complete Intersections (Paperback, 1st ed. 2016): David Eisenbud, Irena Peeva Minimal Free Resolutions over Complete Intersections (Paperback, 1st ed. 2016)
David Eisenbud, Irena Peeva
R796 Discovery Miles 7 960 Ships in 12 - 17 working days

This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957. The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics.

3264 and All That - A Second Course in Algebraic Geometry (Paperback): David Eisenbud, Joe Harris 3264 and All That - A Second Course in Algebraic Geometry (Paperback)
David Eisenbud, Joe Harris
R917 Discovery Miles 9 170 Ships in 12 - 17 working days

This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles' nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincare's development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics.

Commutative Algebra - with a View Toward Algebraic Geometry (Paperback, 1st ed. 1995. Corr. 3rd printing 1999): David Eisenbud Commutative Algebra - with a View Toward Algebraic Geometry (Paperback, 1st ed. 1995. Corr. 3rd printing 1999)
David Eisenbud
R1,022 R968 Discovery Miles 9 680 Save R54 (5%) Ships in 10 - 20 working days

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.

The Geometry of Schemes (Hardcover, 2000 ed.): David Eisenbud, Joe Harris The Geometry of Schemes (Hardcover, 2000 ed.)
David Eisenbud, Joe Harris
R2,223 Discovery Miles 22 230 Ships in 7 - 11 working days

The theory of schemes is the foundation for algebraic geometry proposed and elaborated by Alexander Grothendieck and his coworkers. It has allowed major progress in classical areas of algebraic geometry such as invariant theory and the moduli of curves. It integrates algebraic number theory with algebraic geometry, fulfilling the dreams of earlier generations of number theorists. This integration has led to proofs of some of the major conjectures in number theory (Deligne's proof of the Weil Conjectures, Faltings proof of the Mordell Conjecture).This book is intended to bridge the chasm between a first course in classical algebraic geometry and a technical treatise on schemes. It focuses on examples, and strives to show "what is going on" behind the definitions. There are many exercises to test and extend the reader's understanding. The prerequisites are modest: a little commutative algebra and an acquaintance with algebraic varieties, roughly at the level of a one-semester course. The book aims to show schemes in relation to other geometric ideas, such as the theory of manifolds. Some familiarity with these ideas is helpful, though not required.

Computations in Algebraic Geometry with Macaulay 2 (Hardcover, 2002 ed.): David Eisenbud, Daniel R. Grayson, Mike Stillman,... Computations in Algebraic Geometry with Macaulay 2 (Hardcover, 2002 ed.)
David Eisenbud, Daniel R. Grayson, Mike Stillman, Bernd Sturmfels
R2,007 R1,201 Discovery Miles 12 010 Save R806 (40%) Ships in 12 - 17 working days

This book presents algorithmic tools for algebraic geometry and experimental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. These expositions will be valuable to both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all. The first part of the book is primarily concerned with introducing Macaulay2, whereas the second part emphasizes the mathematics.

Computations in Algebraic Geometry with Macaulay 2 (Paperback, Softcover reprint of the original 1st ed. 2002): David Eisenbud,... Computations in Algebraic Geometry with Macaulay 2 (Paperback, Softcover reprint of the original 1st ed. 2002)
David Eisenbud, Daniel R. Grayson, Mike Stillman, Bernd Sturmfels
R1,910 Discovery Miles 19 100 Ships in 7 - 11 working days

Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Re cently developed algorithms have made theoretical aspects of the subject accessible to a broad range of mathematicians and scientists. The algorith mic approach to the subject has two principal aims: developing new tools for research within mathematics, and providing new tools for modeling and solv ing problems that arise in the sciences and engineering. A healthy synergy emerges, as new theorems yield new algorithms and emerging applications lead to new theoretical questions. This book presents algorithmic tools for algebraic geometry and experi mental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. A wide range of mathematical scientists should find these expositions valuable. This includes both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all."

The Geometry of Syzygies - A Second Course in Algebraic Geometry and Commutative Algebra (Hardcover, 2005 ed.): David Eisenbud The Geometry of Syzygies - A Second Course in Algebraic Geometry and Commutative Algebra (Hardcover, 2005 ed.)
David Eisenbud
R2,201 Discovery Miles 22 010 Ships in 7 - 11 working days

Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and problems. This side of the subject can be approached through the equations of a variety, and the syzygies of these equations are a necessary part of the study. This book is the first textbook-level account of basic examples and techniques in this area. It illustrates the use of syzygies in many concrete geometric considerations, from interpolation to the study of canonical curves. The text has served as a basis for graduate courses by the author at Berkeley, Brandeis, and in Paris. It is also suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. As an aid to the reader, the appendices provide summaries of local cohomology and commutative algebra, tying together examples and major results from a wide range of topics.

The Geometry of Syzygies - A Second Course in Algebraic Geometry and Commutative Algebra (Paperback, 2005 ed.): David Eisenbud The Geometry of Syzygies - A Second Course in Algebraic Geometry and Commutative Algebra (Paperback, 2005 ed.)
David Eisenbud
R1,163 Discovery Miles 11 630 Ships in 7 - 11 working days

Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and problems. This side of the subject can be approached through the equations of a variety, and the syzygies of these equations are a necessary part of the study. This book is the first textbook-level account of basic examples and techniques in this area. It illustrates the use of syzygies in many concrete geometric considerations, from interpolation to the study of canonical curves. The text has served as a basis for graduate courses by the author at Berkeley, Brandeis, and in Paris. It is also suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. As an aid to the reader, the appendices provide summaries of local cohomology and commutative algebra, tying together examples and major results from a wide range of topics.

Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110), Volume 110 (Paperback): David Eisenbud,... Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110), Volume 110 (Paperback)
David Eisenbud, Walter D. Neumann
R1,488 R1,154 Discovery Miles 11 540 Save R334 (22%) Ships in 12 - 17 working days

This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction is a method of obtaining any link by "splicing" links of the simplest kinds, namely those whose exteriors are Seifert fibered or hyperbolic. This approach to link theory is particularly attractive since most invariants of links are additive under splicing. Specially distinguished from this viewpoint is the class of links, none of whose splice components is hyperbolic. It includes all links constructed by cabling and connected sums, in particular all links of singularities of complex plane curves. One of the main contributions of this monograph is the calculation of invariants of these classes of links, such as the Alexander polynomials, monodromy, and Seifert forms.

The Geometry of Schemes (Paperback, 1st ed. 2000. Corr. 2nd printing 2001): David Eisenbud, Joe Harris The Geometry of Schemes (Paperback, 1st ed. 2000. Corr. 2nd printing 2001)
David Eisenbud, Joe Harris
R1,782 Discovery Miles 17 820 Ships in 7 - 11 working days

The theory of schemes is the foundation for algebraic geometry proposed and elaborated by Alexander Grothendieck and his co-workers. It has allowed major progress in classical areas of algebraic geometry such as invariant theory and the moduli of curves. It integrates algebraic number theory with algebraic geometry, fulfilling the dreams of earlier generations of number theorists. This integration has led to proofs of some of the major conjectures in number theory (Deligne's proof of the Weil Conjectures, Faltings' proof of the Mordell Conjecture). This book is intended to bridge the chasm between a first course in classical algebraic geometry and a technical treatise on schemes. It focuses on examples, and strives to show "what is going on" behind the definitions. There are many exercises to test and extend the reader's understanding. The prerequisites are modest: a little commutative algebra and an acquaintance with algebraic varieties, roughly at the level of a one-semester course. The book aims to show schemes in relation to other geometric ideas, such as the theory of manifolds. Some familiarity with these ideas is helpful, though not required.

Commutative Algebra - with a View Toward Algebraic Geometry (Hardcover): David Eisenbud Commutative Algebra - with a View Toward Algebraic Geometry (Hardcover)
David Eisenbud
R2,228 Discovery Miles 22 280 Ships in 7 - 11 working days

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.

Free Resolutions in Commutative Algebra and Algebraic Geometry (Paperback, New): David Eisenbud, Craig Huneke Free Resolutions in Commutative Algebra and Algebraic Geometry (Paperback, New)
David Eisenbud, Craig Huneke
R1,040 R928 Discovery Miles 9 280 Save R112 (11%) Out of stock

The selected contributions in this volume originated at the Sundance conference, which was devoted to discussions of current work in the area of free resolutions. The papers include new research, not otherwise published, and expositions that develop current problems likely to influence future developments in the field.

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