Introduction to singularities and deformations

著者

• Greuel, G.-M. (Gert-Martin)
• Lossen, Christoph
• Shustin, Eugenii

書誌事項

Introduction to singularities and deformations

G.-M. Greuel, C. Lossen, E. Shustin

（Springer monographs in mathematics）

Springer, c2007

注記

"This text has grown up from a preparatory part of our monograph Singular algebraic curves (to appear), ..."--Pref., p. [vii]

Includes bibliographical references (p. [447]-453) and index

内容説明・目次

内容説明

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.

目次

I. Singularity Theory.- Basic Properties of Complex Spaces and Germs.- Weierstrass Preparation and Finiteness Theorem.- Application to Analytic Algebras.- Complex Spaces.- Complex Space Germs and Singularities.- Finite Morphisms and Finite Coherence Theorem.- Applications of the Finite Coherence Theorem.- Finite Morphisms and Flatness.- Flat Morphisms and Fibres.- Singular Locus and Differential Forms.- Hypersurface Singularities.- Invariants of Hypersurface Singularities.- Finite Determinacy.- Algebraic Group Actions.- Classification of Simple Singularities.- Plane Curve Singularities.- Parametrization.- Intersection Multiplicity.- Resolution of Plane Curve Singularities.- Classical Topological and Analytic Invariants II. Local Deformation Theory.- Deformations of Complex Space Germs.- Deformations of Singularities.- Embedded Deformations.- Versal Deformations.- Infinitesimal Deformations.- Obstructions.- Equisingular Deformations of Plane Curve Singularities.- Equisingular Deformations of the Equation.- The Equisingularity Ideal.- Deformations of the Parametrization.- Computation of T^1 and T^2 .- Equisingular Deformations of the Parametrization.- Equinormalizable Deformations.- Versal Equisingular Deformations.-Appendices: Sheaves.- Commutative Algebra.- Formal Deformation Theory.- Literature.- Index

「Nielsen BookData」 より

• NII書誌ID(NCID): BA79709999
• ISBN:
  • 9783540283805
• LCCN: 2006935374
• 出版国コード: gw
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Berlin
• ページ数/冊数: xii, 471 p.
• 大きさ: 24 cm
• 分類:
  • LCC : QC20.7.S54
  • DC22 : 515/.942
• 件名:
  • LCSH : Singularities (Mathematics)
  • LCSH : Deformations of singularities
• 親書誌ID:
  • BA3386797X