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Resolution of Curve and Surface Singularities in Characteristic Zero (Paperback, Softcover reprint of hardcover 1st ed. 2004) Loot Price: R2,702
Discovery Miles 27 020

# Resolution of Curve and Surface Singularities in Characteristic Zero (Paperback, Softcover reprint of hardcover 1st ed. 2004)

## K. Kiyek, J.L. Vicente

### Series: Algebra and Applications, 4

Loot Price R2,702 Discovery Miles 27 020

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The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. ** . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it * To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.

### General

 Imprint: Springer Country of origin: Netherlands Series: Algebra and Applications, 4 Release date: December 2010 First published: 2004 Authors: K. Kiyek • J.L. Vicente Dimensions: 235 x 155 x 25mm (L x W x T) Format: Paperback Pages: 486 Edition: Softcover reprint of hardcover 1st ed. 2004 ISBN-13: 978-90-481-6573-5 Categories: Books > Science & Mathematics > Mathematics Books > Science & Mathematics > Mathematics > Algebra Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis Books > Science & Mathematics > Mathematics > Geometry Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry LSN: 90-481-6573-3 Barcode: 9789048165735

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