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Compactifying Moduli Spaces 1st ed. 2016 [Mīkstie vāki]

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  • Formāts: Paperback / softback, 135 pages, height x width: 240x168 mm, weight: 2537 g, 1 Illustrations, color; VII, 135 p. 1 illus. in color., 1 Paperback / softback
  • Sērija : Advanced Courses in Mathematics - CRM Barcelona
  • Izdošanas datums: 12-Feb-2016
  • Izdevniecība: Birkhauser Verlag AG
  • ISBN-10: 3034809204
  • ISBN-13: 9783034809207
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Compactifying Moduli Spaces 1st ed. 2016Palielināt
  • Formāts: Paperback / softback, 135 pages, height x width: 240x168 mm, weight: 2537 g, 1 Illustrations, color; VII, 135 p. 1 illus. in color., 1 Paperback / softback
  • Sērija : Advanced Courses in Mathematics - CRM Barcelona
  • Izdošanas datums: 12-Feb-2016
  • Izdevniecība: Birkhauser Verlag AG
  • ISBN-10: 3034809204
  • ISBN-13: 9783034809207
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783034809207.html
Keywords:
This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated.

Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to construct and compactify moduli spaces are presented. In the second, some questions on the boundary of moduli spaces of surfaces are addressed. Finally, the theory of stable quotients is explained, which yields meaningful compactifications of moduli spaces of maps.

Both advanced graduate students and researchers in algebraic geometry will find this book a valuable read.
Foreword vii
1 Perspectives on the Construction and Compactification of Moduli Spaces
Radu Laza
Introduction
1(2)
1.1 The GIT approach to constructing moduli spaces
3(8)
1.1.1 Basic GIT and moduli
3(6)
1.1.2 Applications of GIT to moduli
9(2)
1.2 Moduli and periods
11(12)
1.2.1 Period maps
12(4)
1.2.2 Applications of locally symmetric varieties
16(3)
1.2.3 Comparison to GIT compactifications
19(4)
1.3 The KSBA approach to moduli spaces
23(18)
1.3.1 The KSBA approach
24(4)
1.3.2 Sic singularities are Du Bois
28(1)
1.3.3 Asymptotic stability, K-stability, and KSBA
29(2)
Bibliography
31(10)
2 Compact Moduli Spaces of Surfaces and Exceptional Vector Bundles
Paul Hacking
Introduction
41(2)
2.1 Moduli spaces of surfaces of general type
43(10)
2.1.1 Surfaces of general type
43(1)
2.1.2 Simultaneous resolution of Du Val singularities
44(1)
2.1.3 Moduli
45(1)
2.1.4 Expected dimension
46(1)
2.1.5 Compactification
47(1)
2.1.6 Stable surfaces
47(1)
2.1.7 Semi-log canonical singularities
47(1)
2.1.8 Dualizing sheaf
47(1)
2.1.9 The index of an sic singularity
48(1)
2.1.10 The index-one cover
49(1)
2.1.11 Q-Gorenstein families of stable surfaces
49(2)
2.1.12 The relative dualizing sheaf
51(2)
2.1.13 Definition of the moduli space M k2,x of stable surfaces
53(1)
2.2 Wahl singularities
53(4)
2.2.1 Degenerations with Wahl singularities define boundary divisors of the moduli space M k2,x
54(1)
2.2.2 Topology of Wahl degenerations
55(2)
2.3 Examples of degenerations of Wahl type
57(4)
2.4 Exceptional vector bundles associated to Wahl degenerations
61(2)
2.5 Examples
63(6)
2.5.1 Del Pezzo surfaces
63(2)
2.5.2 Godeaux surfaces
65(1)
Bibliography
66(3)
3 Notes on the Moduli Space of Stable Quotients
Dragos Oprea
Introduction
69(1)
3.1 Morphism spaces and Quot schemes over a fixed curve
70(15)
3.1.1 Stable maps
71(1)
3.1.2 Quot schemes
72(1)
3.1.3 Comparison
73(2)
3.1.4 Smoothness
75(7)
3.1.5 Intersections
82(3)
3.2 Stable quotients
85(17)
3.2.1 Definition of stable quotients and examples
85(6)
3.2.2 Construction of the moduli space
91(2)
3.2.3 Obstruction theory
93(2)
3.2.4 Invariants
95(1)
3.2.5 Virtually smooth morphisms and comparison of invariants
95(7)
3.3 Stable quotient invariants
102(19)
3.3.1 Equivariant localization
102(3)
3.3.2 Local geometries
105(11)
3.3.3 Hypersurface geometries
116(5)
3.4 Wall-crossing and other geometries
121
3.4.1 Variation of stability
121(3)
3.4.2 Quasimaps to GIT quotients
124(5)
3.4.3 Quasimap invariants of semi-positive GIT targets
129(4)
Bibliography
133