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Resolution of Singularities of Embedded Algebraic Surfaces (Springer Monographs in Mathematics) - Hardcover
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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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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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Resolution of Singularities of Embedded Algebraic Surfaces (Springer Monographs in Mathematics)
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Resolution of Singularities of Embedded Algebraic Surfaces
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RESOLUTION OF SINGULARITIES OF EMBEDDED ALGEBRAIC SURFACES
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Hardcover. Second, Enlarged Edition. Octavo, xii, 311 pages. In Very Good minus condition. Spine is yellow and green with white lettering. Light bumping to foot edge of front and back boards. Light water damage to back cover. NOTE: Shelved in Netdesk Column R (ND-R). 1378331. FP New Rockville Stock. Artikel-Nr. 1378331
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Resolution of Singularities of Embedded Algebraic Surfaces (Springer Monographs in Mathematics)
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Resolution of Singularities of Embedded Algebraic Surfaces
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Gebunden. Zustand: New. Description of the author s proof of desingularization of algebraic surfaces Self-contained introduction to birational algebraic geometry, based only on basic commutative algebra. The unique place where desigularization for solids in characteristic p is don. Artikel-Nr. 4896472
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Resolution of Singularities of Embedded Algebraic Surfaces
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Zustand: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher. Artikel-Nr. 67422/2
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Resolution of Singularities of Embedded Algebraic Surfaces
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Springer, Berlin, Springer Berlin Heidelberg, Springer, 1998
ISBN 10: 3540637192
ISBN 13: 9783540637196
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Buch. Zustand: Neu. Neuware - 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. Artikel-Nr. 9783540637196
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