Resolution of Curve and Surface Singularities in Characteristic Zero

Language: English

Published by Springer, Springer, 2010

9048165733 / 9789048165735

Series: Book 4 of 29 - Algebra and Applications

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Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH

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Druck auf Anfrage Neuware - Printed after ordering - 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}.

Seller Inventory # 9789048165735

Title
Resolution of Curve and Surface Singularities in Characteristic Zero
Author
K. Kiyek
Publisher
Springer, Springer
Publication year
2010
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
9048165733
ISBN 13
9789048165735
Item weight
762 grams
Dimensions
235x155x28 mm
Series
Book 4 of 29: Algebra and Applications

AHA-BUCH GmbH

Einbeck, Germany

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AbeBooks seller since August 14, 2006

Shipping rates from Germany to U.S.A.

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