Resolution of Singularities of Embedded Algebraic Surfaces - Rilegato

Abhyankhar, S.

 
9783540637196: Resolution of Singularities of Embedded Algebraic Surfaces
Rilegato
ISBN 10: 3540637192 ISBN 13: 9783540637196
Casa editrice: Springer Verlag, 1998

Sinossi

The common solutions of a finite number of polynomial equations in a finite number of variables constitute an algebraic variety. The degrees of freedom of a moving point on the variety is the dimension of the variety. A one-dimensional variety is a curve and a two-dimensional variety is a surface. A three-dimensional variety may be called asolid. Most points of a variety are simple points. Singularities are special points, or points of multiplicity greater than one. Points of multiplicity two are double points, points of multiplicity three are tripie points, and so on. A nodal point of a curve is a double point where the curve crosses itself, such as the alpha curve. A cusp is a double point where the curve has a beak. The vertex of a cone provides an example of a surface singularity. A reversible change of variables gives abirational transformation of a variety. Singularities of a variety may be resolved by birational transformations.

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Dalla quarta di copertina

This new edition describes the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic. The book also provides a self-contained introduction to birational algebraic geometry, based only on basic commutative algebra. In addition, it gives a short proof of analytic desingularization in characteristic zero for any dimension found in 1996 and based on a new avatar of an algorithmic trick employed in the original edition of the book. This new edition will inspire further progress in resolution of singularities of algebraic and arithmetical varieties which will be valuable for applications to algebraic geometry and number theory. It can can be used for a second year graduate course. The reference list has been updated.

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Editore
Springer Verlag
Data di pubblicazione
1998
Lingua
Inglese
ISBN 10 
3540637192
ISBN 13 
9783540637196
Rilegatura
Copertina rigida
Numero di pagine
311
Contatto del produttore
non disponibile
Persona responsabile
Springer Nature Customer Service Center GmbH
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Heidelberg
69115
Germania

Altre edizioni note dello stesso titolo

9783642083518: Resolution of Singularities of Embedded Algebraic Surfaces

Edizione in evidenza

ISBN 10:  364208351X ISBN 13:  9783642083518
Casa editrice: Springer, 2010
Brossura