"This book will be an excellent resource for mathematicians and graduate students in algebraic geometry and representation theory of algebraic groups."--BOOK JACKET.
Preface
vii
1 Frobenius Splitting: General Theory
1
(58)
1.1 Basic definitions, properties, and examples
2
(10)
1.2 Consequences of Frobenius splitting
12
(8)
1.3 Criteria for splitting
20
(15)
1.4 Splitting relative to a divisor
35
(6)
1.5 Consequences of diagonal splitting
41
(12)
1.6 From characteristic ρ to characteristic 0
53
(6)
2 Frobenius Splitting of Schubert Varieties
59
(24)
2.1 Notation
60
(4)
2.2 Frobenius splitting of the BSDH varieties Ζτupsilon
64
(8)
2.3 Some more splittings of G/B and G/B x G/B
72
(11)
3 Cohomology and Geometry of Schubert Varieties
83
(26)
3.1 Cohomology of Schubert varieties
85
(6)
3.2 Normality of Schubert varieties
91
(4)
3.3 Demazure character formula
95
(5)
3.4 Schubert varieties have rational resolutions
100
(3)
3.5 Homogeneous coordinate rings of Schubert varieties are Koszul algebras
103
(6)
4 Canonical Splitting and Good Filtration
109
(44)
4.1 Canonical splitting
111
(13)
4.2 Good filtrations
124
(18)
4.3 Proof of the PRVK conjecture and its refinement
142
(11)
5 Cotangent Bundles of Flag Varieties
153
(30)
5.1 Splitting of cotangent bundles of flag varieties
155
(14)
5.2 Cohomology vanishing of cotangent bundles of flag varieties
169
(9)
5.3 Geometry of the nilpotent and subregular cones
178
(5)
6 Equivariant Embeddings of Reductive Groups
183
(24)
6.1 The wonderful compactification
184
(13)
6.2 Reductive embeddings
197
(10)
7 Hilbert Schemes of Points on Surfaces
207
(24)
7.1 Symmetric products
208
(8)
7.2 Hilbert schemes of points
216
(4)
7.3 The Hilbert-Chow morphism
220
(4)
7.4 Hilbert schemes of points on surfaces
224
(3)
7.5 Splitting of Hilbert schemes of points on surfaces
227
(4)
Bibliography
231
(16)
Index
247
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