Resolution of Singularities of Embedded Algebraic Surfaces (Paperback, Softcover reprint of hardcover 2nd ed. 1998)

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.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Springer Monographs in Mathematics
Release date:	December 2010
First published:	1998
Authors:	Shreeram S. Abhyankar
Dimensions:	235 x 155 x 17mm (L x W x T)
Format:	Paperback
Pages:	312
Edition:	Softcover reprint of hardcover 2nd ed. 1998
ISBN-13:	978-3-642-08351-8
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Books > Science & Mathematics > Mathematics > Number theory > General
LSN:	3-642-08351-X
Barcode:	9783642083518

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