Singular algebraic curves: with an appendix by oleg viro

Gert-Martin / Lossen Greuel

553 pages, parution le 02/03/2019

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Résumé

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.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.

Zero-Dimensional Schemes for Singularities.- Global Deformation Theory.- H ¹ -Vanishing Theorems.- Equisingular Families of Curves.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Gert-Martin / Lossen Greuel
Parution	02/03/2019
Nb. de pages	553
Couverture	Broché
EAN13	9783030033491

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Singular algebraic curves: with an appendix by oleg viro

Résumé

Caractéristiques techniques

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