Classifying spaces of degenerating polarized Hodge structures /

In 1970, Philip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. In this book, Kato and Usui realize this dream by creating a logarithmic Hodge theory.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Kato, K. (Kazuya)
Otros Autores: Usui, Sampei
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, N.J. : Princeton University Press, 2009.
Colección:Annals of mathematics studies ; no. 169.
Temas:
Hodge theory.
Logarithms.
Théorie de Hodge.
Logarithmes.
logarithms.
MATHEMATICS > Topology.
Hodge-Struktur
Hodge-Theorie
Logarithmus
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 0.1 Hodge Theory 7
  • 0.2 Logarithmic Hodge Theory 11
  • 0.3 Griffiths Domains and Moduli of PH 24
  • 0.4 Toroidal Partial Compactifications of [Gamma]/D and Moduli of PLH 30
  • 0.5 Fundamental Diagram and Other Enlargements of D 43
  • 0.7 Notation and Convention 67
  • Chapter 1 Spaces of Nilpotent Orbits and Spaces of Nilpotent i-Orbits 70
  • 1.1 Hodge Structures and Polarized Hodge Structures 70
  • 1.2 Classifying Spaces of Hodge Structures 71
  • 1.3 Extended Classifying Spaces 72
  • Chapter 2 Logarithmic Hodge Structures 75
  • 2.1 Logarithmic Structures 75
  • 2.2 Ringed Spaces (X[superscript log], O[subscript X superscript log]) 81
  • 2.3 Local Systems on X[superscript log] 88
  • 2.4 Polarized Logarithmic Hodge Structures 94
  • 2.5 Nilpotent Orbits and Period Maps 97
  • 2.6 Logarithmic Mixed Hodge Structures 105
  • Chapter 3 Strong Topology and Logarithmic Manifolds 107
  • 3.1 Strong Topology 107
  • 3.2 Generalizations of Analytic Spaces 115
  • 3.3 Sets E[subscript sigma] and E[subscript sigma superscript sharp] 120
  • 3.4 Spaces E[subscript sigma], [Gamma]/D[subscript Sigma], E[subscript sigma superscript sharp], and D[subscript Sigma superscript sharp] 125
  • 3.5 Infinitesimal Calculus and Logarithmic Manifolds 127
  • 3.6 Logarithmic Modifications 133
  • Chapter 4 Main Results 146
  • 4.1 Theorem A: The Spaces E[subscript sigma], [Gamma]/D[subscript Sigma], and [Gamma]/D[subscript Sigma sharp] 146
  • 4.2 Theorem B: The Functor PLH[subscript phi] 147
  • 4.3 Extensions of Period Maps 148
  • 4.4 Infinitesimal Period Maps 153
  • Chapter 5 Fundamental Diagram 157
  • 5.1 Borel-Serre Spaces (Review) 158
  • 5.2 Spaces of SL(2)-Orbits (Review) 165
  • 5.3 Spaces of Valuative Nilpotent Orbits 170
  • 5.4 Valuative Nilpotent i-Orbits and SL(2)-Orbits 173
  • Chapter 6 The Map [psi] : D[subscript val superscript sharp] to D[subscript SL] (2) 175
  • 6.1 Review of [CKS] and Some Related Results 175
  • 6.2 Proof of Theorem 5.4.2 186
  • 6.3 Proof of Theorem 5.4.3 (i) 190
  • 6.4 Proofs of Theorem 5.4.3 (ii) and Theorem 5.4.4 195
  • Chapter 7 Proof of Theorem A 205
  • 7.1 Proof of Theorem A (i) 205
  • 7.2 Action of [sigma subscript C] on E[subscript sigma] 209
  • 7.3 Proof of Theorem A for [Gamma]([sigma])[superscript gp]/D[subscript sigma] 215
  • 7.4 Proof of Theorem A for [Gamma]/D[subscript Sigma] 220
  • Chapter 8 Proof of Theorem B 226
  • 8.1 Logarithmic Local Systems 226
  • 8.2 Proof of Theorem B 229
  • 8.3 Relationship among Categories of Generalized Analytic Spaces 235
  • 8.4 Proof of Theorem 0.5.29 241
  • Chapter 9 [flat]-Spaces 244
  • 9.1 Definitions and Main Properties 244
  • 9.2 Proofs of Theorem 9.1.4 for [Gamma]/X[subscript BS superscript flat], [Gamma]/D[superscript flat subscript BS], and [Gamma]/D[subscript BS, val superscript flat] 246
  • 9.3 Proof of Theorem 9.1.4 for [Gamma]/D[subscript SL(2), less than or equal 1 superscript flat] 248
  • 9.4 Extended Period Maps 249
  • Chapter 10 Local Structures of D[subscript SL(2)] and [Gamma]/D[subscript SL(2), less than or equal 1 superscript flat] 251
  • 10.1 Local Structures of D[subscript SL(2)] 251
  • 10.2 A Special Open Neighborhood U(p) 255
  • 10.3 Proof of Theorem 10.1.3 263
  • 10.4 Local Structures of D[subscript SL(2), less than or equal 1] and [Gamma]/D[subscript SL(2), less than or equal 1 superscript flat] 269
  • Chapter 11 Moduli of PLH with Coefficients 271
  • 11.1 Space [Gamma]/D[subscript Sigma superscript A] 271
  • 11.2 PLH with Coefficients 274
  • 11.3 Moduli 275
  • Chapter 12 Examples and Problems 277
  • 12.1 Siegel Upper Half Spaces 277
  • 12.2 Case G[subscript R] [bsime] O(1, n
  • 1, R) 281
  • 12.3 Example of Weight 3 (A) 290
  • 12.4 Example of Weight 3 (B) 295
  • 12.5 Relationship with [U2] 299
  • 12.6 Complete Fans 301
  • 12.7 Problems 304
  • A1 Positive Direction of Local Monodromy 307
  • A2 Proper Base Change Theorem for Topological Spaces 310.

Ejemplares similares