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Algebraic Geometry Salt Lake City 2015 (Part 2) (Hardcover): Tommaso de Fernex, Brendan Hassett, Mircea Mustata, Martin Olsson,... Algebraic Geometry Salt Lake City 2015 (Part 2) (Hardcover)
Tommaso de Fernex, Brendan Hassett, Mircea Mustata, Martin Olsson, Mihnea Popa, …
R3,325 R2,954 Discovery Miles 29 540 Save R371 (11%) Ships in 10 - 15 working days

This is Part 2 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic $p$ and $p$-adic tools, etc. The resulting articles will be important references in these areas for years to come.

Algebraic Geometry Salt Lake City 2015 (Part 1) (Hardcover): Tommaso de Fernex, Brendan Hassett, Mircea Mustata, Martin Olsson,... Algebraic Geometry Salt Lake City 2015 (Part 1) (Hardcover)
Tommaso de Fernex, Brendan Hassett, Mircea Mustata, Martin Olsson, Mihnea Popa, …
R3,329 R2,958 Discovery Miles 29 580 Save R371 (11%) Ships in 10 - 15 working days

This is Part 1 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic $p$ and $p$-adic tools, etc. The resulting articles will be important references in these areas for years to come.

Brauer Groups and Obstruction Problems - Moduli Spaces and Arithmetic (Hardcover, 1st ed. 2017): Asher Auel, Brendan Hassett,... Brauer Groups and Obstruction Problems - Moduli Spaces and Arithmetic (Hardcover, 1st ed. 2017)
Asher Auel, Brendan Hassett, Anthony Varilly-Alvarado, Bianca Viray
R2,816 R2,388 Discovery Miles 23 880 Save R428 (15%) Ships in 10 - 15 working days

The contributions in this book explore various contexts in which the derived category of coherent sheaves on a variety determines some of its arithmetic. This setting provides new geometric tools for interpreting elements of the Brauer group. With a view towards future arithmetic applications, the book extends a number of powerful tools for analyzing rational points on elliptic curves, e.g., isogenies among curves, torsion points, modular curves, and the resulting descent techniques, as well as higher-dimensional varieties like K3 surfaces. Inspired by the rapid recent advances in our understanding of K3 surfaces, the book is intended to foster cross-pollination between the fields of complex algebraic geometry and number theory. Contributors: * Nicolas Addington * Benjamin Antieau * Kenneth Ascher * Asher Auel * Fedor Bogomolov * Jean-Louis Colliot-Thelene * Krishna Dasaratha * Brendan Hassett * Colin Ingalls * Marti Lahoz * Emanuele Macri * Kelly McKinnie * Andrew Obus * Ekin Ozman * Raman Parimala * Alexander Perry * Alena Pirutka * Justin Sawon * Alexei N. Skorobogatov * Paolo Stellari * Sho Tanimoto * Hugh Thomas * Yuri Tschinkel * Anthony Varilly-Alvarado * Bianca Viray * Rong Zhou

Algebraic Geometry Salt Lake City 2015 (Parts 1 and 2) (Hardcover): Tommaso de Fernex, Brendan Hassett, Mircea Mustata, Martin... Algebraic Geometry Salt Lake City 2015 (Parts 1 and 2) (Hardcover)
Tommaso de Fernex, Brendan Hassett, Mircea Mustata, Martin Olsson, Mihnea Popa, …
R6,444 R5,559 Discovery Miles 55 590 Save R885 (14%) Ships in 10 - 15 working days

Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. These volumes include surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic $p$ and $p$-adic tools, etc. The resulting articles will be important references in these areas for years to come.

Brauer Groups and Obstruction Problems - Moduli Spaces and Arithmetic (Paperback, Softcover reprint of the original 1st ed.... Brauer Groups and Obstruction Problems - Moduli Spaces and Arithmetic (Paperback, Softcover reprint of the original 1st ed. 2017)
Asher Auel, Brendan Hassett, Anthony Varilly-Alvarado, Bianca Viray
R3,175 Discovery Miles 31 750 Ships in 7 - 11 working days

The contributions in this book explore various contexts in which the derived category of coherent sheaves on a variety determines some of its arithmetic. This setting provides new geometric tools for interpreting elements of the Brauer group. With a view towards future arithmetic applications, the book extends a number of powerful tools for analyzing rational points on elliptic curves, e.g., isogenies among curves, torsion points, modular curves, and the resulting descent techniques, as well as higher-dimensional varieties like K3 surfaces. Inspired by the rapid recent advances in our understanding of K3 surfaces, the book is intended to foster cross-pollination between the fields of complex algebraic geometry and number theory. Contributors: * Nicolas Addington * Benjamin Antieau * Kenneth Ascher * Asher Auel * Fedor Bogomolov * Jean-Louis Colliot-Thelene * Krishna Dasaratha * Brendan Hassett * Colin Ingalls * Marti Lahoz * Emanuele Macri * Kelly McKinnie * Andrew Obus * Ekin Ozman * Raman Parimala * Alexander Perry * Alena Pirutka * Justin Sawon * Alexei N. Skorobogatov * Paolo Stellari * Sho Tanimoto * Hugh Thomas * Yuri Tschinkel * Anthony Varilly-Alvarado * Bianca Viray * Rong Zhou

Geometry Over Nonclosed Fields (Paperback, Softcover reprint of the original 1st ed. 2017): Fedor Bogomolov, Brendan Hassett,... Geometry Over Nonclosed Fields (Paperback, Softcover reprint of the original 1st ed. 2017)
Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel
R3,796 Discovery Miles 37 960 Ships in 7 - 11 working days

Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail.

Introduction to Algebraic Geometry (Paperback): Brendan Hassett Introduction to Algebraic Geometry (Paperback)
Brendan Hassett
R1,104 Discovery Miles 11 040 Ships in 7 - 11 working days

Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Grobner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.

Arithmetic Geometry (Paperback): Henri Darmon, David A. Ellwood, Brendan Hassett, Yuri Tschinkel Arithmetic Geometry (Paperback)
Henri Darmon, David A. Ellwood, Brendan Hassett, Yuri Tschinkel
R2,986 Discovery Miles 29 860 Out of stock

This book is based on survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the University of Gottingen. Intended for graduate students and recent Ph.D.'s, this volume will introduce readers to modern techniques and outstanding conjectures at the interface of number theory and algebraic geometry. The main focus is rational points on algebraic varieties over non-algebraically closed fields. Do they exist? If not, can this be proven efficiently and algorithmically? When rational points do exist, are they finite in number and can they be found effectively? When there are infinitely many rational points, how are they distributed? For curves, a cohesive theory addressing these questions has emerged in the last few decades. Highlights include Faltings' finiteness theorem and Wiles' proof of Fermat's Last Theorem. Key techniques are drawn from the theory of elliptic curves, including modular curves and parametrizations, Heegner points, and heights. The arithmetic of higher-dimensional varieties is equally rich, offering a complex interplay of techniques including Shimura varieties, the minimal model program, moduli spaces of curves and maps, deformation theory, Galois cohomology, harmonic analysis, and automorphic functions. However, many foundational questions about the structure of rational points remain open, and research tends to focus on properties of specific classes of varieties.

A Celebration of Algebraic Geometry (Paperback): Brendan Hassett, James McKernan, Jason Starr, Ravi Vakil A Celebration of Algebraic Geometry (Paperback)
Brendan Hassett, James McKernan, Jason Starr, Ravi Vakil
R2,878 Discovery Miles 28 780 Out of stock

This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honour of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkahler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry.

Geometry Over Nonclosed Fields (Hardcover, 1st ed. 2017): Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel Geometry Over Nonclosed Fields (Hardcover, 1st ed. 2017)
Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel
R3,476 Discovery Miles 34 760 Out of stock

Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail.

Rationality Problems in Algebraic Geometry - Levico Terme, Italy 2015 (Paperback, 1st ed. 2016): Rita Pardini, Gian Pietro... Rationality Problems in Algebraic Geometry - Levico Terme, Italy 2015 (Paperback, 1st ed. 2016)
Rita Pardini, Gian Pietro Pirola; Arnaud Beauville, Brendan Hassett, Alexander Kuznetsov, …
R864 Discovery Miles 8 640 Out of stock

Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel-Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.

Birational Geometry, Rational Curves, and Arithmetic (Hardcover, 2013 ed.): Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel Birational Geometry, Rational Curves, and Arithmetic (Hardcover, 2013 ed.)
Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel
R2,453 Discovery Miles 24 530 Out of stock

This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

Birational Geometry, Rational Curves, and Arithmetic (Paperback, 2013 ed.): Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel Birational Geometry, Rational Curves, and Arithmetic (Paperback, 2013 ed.)
Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel
R3,764 Discovery Miles 37 640 Out of stock

This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

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