Eugenii Shustin's Books

Singular Algebraic Curves

With an Appendix by Oleg Viro

By: Gert-Martin Greuel,Christoph Lossen,Eugenii Shustin

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Singular Algebraic Curves

With an Appendix by Oleg Viro

By: Gert-Martin Greuel,Christoph Lossen,Eugenii Shustin

Singular algebraic curves have been in the focus of study in algebraic geometry from the very beginning, and till now remain a subject of an active research related to many modern developments in algebraic geometry, symplectic geometry, and tropical geometry. The monograph suggests a unified approach to the geometry of singular algebraic curves on algebraic surfaces and their families, which applies to arbitrary singularities, allows one to treat all main questions concerning the geometry of equisingular families of curves, and, finally, leads to results which can be viewed as the best possible in a reasonable sense. Various methods of the cohomology vanishing theory as well as the patchworking construction with its modifications will be of a special interest for experts in algebraic geometry and singularity theory. The introductory chapters on zero-dimensional schemes and global deformation theory can well serve as a material for special courses and seminars for graduate and post-graduate students.Geometry in general plays a leading role in modern mathematics, and algebraic geometry is the most advanced area of research in geometry. In turn, algebraic curves for more than one century have been the central subject of algebraic geometry both in fundamental theoretic questions and in applications to other fields of mathematics and mathematical physics. Particularly, the local and global study of singular algebraic curves involves a variety of methods and deep ideas from geometry, analysis, algebra, combinatorics and suggests a number of hard classical and newly appeared problems which inspire further development in this research area.

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Page Count

569

Publisher

Springer

Published Date

ISBN 10

3030033503

ISBN 13

9783030033507

Tropical Algebraic Geometry

By: Ilia Itenberg,Grigory Mikhalkin,Eugenii I. Shustin

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Tropical Algebraic Geometry

By: Ilia Itenberg,Grigory Mikhalkin,Eugenii I. Shustin

These notes present a polished introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The notes are based on a seminar at the Mathematical Research Center in Oberwolfach in October 2004. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.

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Page Count

113

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3034600488

ISBN 13

9783034600484

Introduction to Singularities and Deformations

By: Gert-Martin Greuel,Christoph Lossen,Eugenii I. Shustin

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Introduction to Singularities and Deformations

By: Gert-Martin Greuel,Christoph Lossen,Eugenii I. Shustin

Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.

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