Fels G. Cycle spaces of flag domains: a complex geometric viewpoint (Boston, 2006). - ОГЛАВЛЕНИЕ / CONTENTS
Навигация

 
Выставка новых поступлений  |  Поступления иностранных книг в библиотеки СО РАН : 2003 | 2006 |2008
ОбложкаFels G. Cycle spaces of flag domains: a complex geometric viewpoint / Fels G., Huckleberry A., Wolf J.A. - Boston: Birkhauser, 2006. - 339 p. - (Progress in mathematics; Vol. 245). - ISBN 0-8176-4391-5
 

Оглавление / Contents
 
Introduction ................................................... xi

Part I  Introduction to Flag Domain Theory

1   Structure of Complex Flag Manifolds ......................... 5
    1.1 Structure theory and the root decomposition ............. 5
    1.2 Cartan highest weight theory ............................ 9
    1.3 Borel subgroups and subalgebras ........................ 14
    1.4 Parabolic subgroups and subalgebras .................... 17
    1.5 Homogeneous holomorphic vector bundles ................. 20
    1.6 The Bott-Borel-Weil Theorem ............................ 22

2   Real Group Orbits .......................................... 27
    2.1 Bruhat. Lemma and an application ....................... 27
    2.2 Real isotropy .......................................... 28

3   Orbit Structure for Hermitian Symmetric Spaces ............. 31
    3.1 Strongly orthogonal roots .............................. 31
    3.2 Orbits and Cayley transforms ........................... 33

4   Open Orbits ................................................ 37
    4.1 Automorphisms and regular elements ..................... 37
    4.2 Fundamental Cartan subalgebras and open G0-orbits ...... 38
    4.3 Compact subvarieties of open orbits .................... 40
    4.4 Holomorphic functions .................................. 42
    4.5 Measurabilily of open orbits ........................... 44
    4.6 Background on Levi geometry ............................ 46
    4.7 The exhaustion function for measurable open orbits ..... 50

5   The Cycle Space of a Flag Domain ........................... 55
    5.1 Definitions and first properties ....................... 55
    5.2 The three cases ........................................ 57
    5.3 Cycle spaces of measurable open orbits are Stein ....... 58
    5.4 The cycle space in the hermitian case .................. 60
    5.5 The classical hermitian case ........................... 66


Part II  Cycle Spaces as Universal Domains

6   Universal Domains .......................................... 77
    6.1 Definitions and first properties ....................... 78
    6.2 Adapted structure ...................................... 83
    6.3 Invariant CR structure and pseudoconvexity ............. 84

7   B-Invariant Hypersurfaces in Mz ............................ 93
    7.1 Iwasawa-Borel subgroups and their Schubert varieties ... 94
    7.2 Envelope construction .................................. 96
    7.3 Schubert intersection properties ...................... 101
    7.4 Trace transform ....................................... 104

8   Orbit Duality via Momentum Geometry ....................... 113
    8.1 Coadjoint orbits ...................................... 114
    8.2 The K0-energy function ................................ 116
    8.3 Duality ............................................... 121
    8.4 Orbit ordering ........................................ 123

9   Schubert Slices in the Context of Duality ................. 125
    9.1 Schubert slices in arbitrary G0-orbits ................ 126
    9.2 Supporting hypersurfaces at the boundary of MD ........ 130

10  Analysis of the Boundary of U ............................. 133
    10.1 Preparation .......................................... 135
    10.2 Linearization and the Jordan decomposition ........... 141
    10.3 Characterization of closed orbits .................... 145
    10.4 The slice theorem and related isotropy
         computations ......................................... 148
    10.5 Example: Two-dimensional affine quadric .............. 152
    10.6 sl2 models at generic points of bd(U) ................ 154

11  Invariant Kobayashi-Hyperbolic Stein Domains .............. 163
    11.1 Hyperbolicily of domains in G/K ...................... 164
    11.2 The maximal invariant Kobayashi-hyperbolic Stein
         domain in an sl2-model ............................... 169
    11.3 Maximality and the characterization of cycle
         domains .............................................. 171

12  Cycle Spaces of Lower-Dimensional Orbits .................. 175
    12.1 Definition of cycle space ............................ 176
    12.2 Intersection with Schubert varieties ................. 177
    12.3 Hypersurfaces in the complement of the cycle space ... 180
    12.4 Cycle Spaces of nonclosed orbits ..................... 181
    12.5 Cycle spaces of closed orbits ........................ 182

13  Examples .................................................. 185
    13.1 Cycle spaces of open SL(n; R)-orbits ................. 186
    13.2 Cycle spaces for open SU(p, q; F)-orbits ............. 190
    13.3 Slice methods and trace transforms for SU(2, 1)
         domains .............................................. 198


Part III  Analytic and Geometric Consequences

14  The Double Fibration Transform ............................ 207
    14.1 Double fibration ..................................... 208
    14.2 Pullback ............................................. 208
    14.3 Pushdown ............................................. 209
    14.4 Local G-structure of G0-bundles ...................... 210
    14.5 The Schubert fibration ............................... 211
    14.6 Contractibility of the fiber ......................... 213
    14.7 Unitary representations of real reductive Lie
         groups ............................................... 214

15  Variation of Hodge Structure .............................. 217

16  Cycles in the K3 Period Domain ............................ 225
    16.1 Position of K3 surfaces in the Kodaira
         classification ....................................... 226
    16.2 Three classes of examples ............................ 227
    16.3 Parameterizing K3 surfaces ........................... 231
    16.4 The cycle space MD+ ................................... 234


Part IV  The Full Cycle Space

17  Combinatorics of Normal Bundles of Base Cycles ............ 243
    17.1 Characterization of compact K-orbits ................. 243
    17.2 Base cycles and the arrangement of Borel subgroups ... 244
    17.3 Normal bundles of base cycles ........................ 245
    17.4 Module structure of the tangent space of
         a symmetric space .................................... 247
    17.5 Shift of degree in the cohomology .................... 253
    17.6 Equivariant nitrations ............................... 257

18  Methods for Computing Hl (C; O(E((q + θq)s))) .............. 259
    18.1 Guide lo the computation ............................. 259
    18.2 Root systems and involutions ......................... 260
    18.3 Various Weyl groups .................................. 267
    18.4 Some distinguished weights ........................... 271
    18.5 Computation of Bott-regular weights .................. 277
    18.6 Algorithm for computing the module structure of
         T|C|C(Z) ............................................. 284

19  Classification for Simple g0 with rank f < rank g ......... 289
    19.1  Strategy ............................................ 290
    19.2  The series for g0 = sl(2r; R) ........................ 290
    19.3  The series for g0 = sl(2r + 1; R) .................... 293
    19.4  The series for g0 = so(2p + 1, 2q + 1) ............... 296
    19.5  The case g0 = ε6C4 ................................... 302
    19.6  Preliminaries for the cases where g0 is of complex
          type ................................................ 304
    19.7  The series for g0 = so(2r + 1; C) .................... 305
    19.8  The series for g0 = sp(r; C) ......................... 306
    19.9  The case g0 = f4(C) .................................. 306
    19.10 The case g0 = g2(C) .................................. 306

20  Classification for rank f = rank g ........................ 309
    20.1 The series for g0 = sp(r; R) .......................... 309
    20.2 The series for g0 = so(2p, 2q + 1) .................... 313
    20.3 The case g0 = f4,C3A1 .................................. 317
    20.4 The case g0 = g2,A1A1 .................................. 319
    20.5 Final table .......................................... 321

References .................................................... 323

Index ......................................................... 331

Symbol Index .................................................. 337


 
Выставка новых поступлений  |  Поступления иностранных книг в библиотеки СО РАН : 2003 | 2006 |2008
 

[О библиотеке | Академгородок | Новости | Выставки | Ресурсы | Библиография | Партнеры | ИнфоЛоция | Поиск]
  Пожелания и письма: branch@gpntbsib.ru
© 1997-2024 Отделение ГПНТБ СО РАН (Новосибирск)
Статистика доступов: архив | текущая статистика
 

Документ изменен: Wed Feb 27 14:52:38 2019. Размер: 13,893 bytes.
Посещение N 1555 c 26.04.2010