Introduction to Singularities and Deformations (eBook)

Gert-Martin Greuel, Christoph Lossen, Eugenii I. Shustin (Autoren)

eBook Download: PDF

2007 | 2007
XII, 472 Seiten
Springer Berlin (Verlag)
978-3-540-28419-2 (ISBN)

Infos

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.

Inhalt

Preface 7
Contents 11
I Singularity Theory 13
1 Basic Properties of Complex Spaces and Germs 20
2 Hypersurface Singularities 122
3 Plane Curve Singularities 173
II Local Deformation Theory 233
1 Deformations of Complex Space Germs 234
2 Equisingular Deformations of Plane Curve Singularities 278
A Sheaves 391
A.1 Presheaves and Sheaves 391
A.2 Gluing Sheaves 393
A.3 Sheaves of Rings and Modules 394
A.4 Image and Preimage Sheaf 395
A.5 Algebraic Operations on Sheaves 396
A.6 Ringed Spaces 397
A.7 Coherent Sheaves 399
A.8 Sheaf Cohomology 400
A.9 Cech Cohomology and Comparison 404
B Commutative Algebra 409
B.1 Associated Primes and Primary Decomposition 409
B.2 Dimension Theory 411
B.3 Tensor Product and Flatness 414
B.4 Artin-Rees and Krull Intersection Theorem 418
B.5 The Local Criterion of Flatness 419
B.6 The Koszul Complex 422
B.7 Regular Sequences and Depth 426
B.8 Cohen-Macaulay, Flatness and Fibres 428
B.9 Auslander-Buchsbaum Formula 434
C Formal Deformation Theory 437
C.1 Functors of Artin Rings 437
C.2 Obstructions 443
C.3 The Cotangent Complex 448
C.4 Cotangent Cohomology 453
C.5 Relation to Deformation Theory 455
References 459
Index 467

Produkt-Details

• Erscheint lt. Verlag: 23.2.2007
• Reihe/Serie: Springer Monographs in Mathematics
• Reihe/Serie: Springer Monographs in Mathematics
• Zusatzinfo: XII, 472 p. 54 illus.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Technik
• Schlagworte: Algebra • Complex space germs • deformation theory • Equisingularity • Local and semi-local rings • Plane curve singularities • singularity theory • Versal deformation
• ISBN-10: 3-540-28419-2 / 3540284192
• ISBN-13: 978-3-540-28419-2 / 9783540284192