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.
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, N.J. :
Princeton University Press,
2009.
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| Series: | Annals of mathematics studies ;
no. 169. |
| Subjects: | |
| Online Access: | CONNECT |
MARC
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| 100 | 1 | |a Kato, K. |q (Kazuya) |1 https://id.oclc.org/worldcat/entity/E39PBJhMgV9ywHTBkYXQ4Fx7HC | |
| 245 | 1 | 0 | |a Classifying spaces of degenerating polarized Hodge structures / |c Kazuya Kato and Sampei Usui. |
| 260 | |a Princeton, N.J. : |b Princeton University Press, |c 2009. | ||
| 300 | |a 1 online resource (ix, 336 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Annals of mathematics studies ; |v no. 169 | |
| 504 | |a Includes bibliographical references (pages 315-319) and index. | ||
| 520 | |a 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. | ||
| 505 | 0 | 0 | |g 0.1 |t Hodge Theory |g 7 -- |g 0.2 |t Logarithmic Hodge Theory |g 11 -- |g 0.3 |t Griffiths Domains and Moduli of PH |g 24 -- |g 0.4 |t Toroidal Partial Compactifications of [Gamma]/D and Moduli of PLH |g 30 -- |g 0.5 |t Fundamental Diagram and Other Enlargements of D |g 43 -- |g 0.7 |t Notation and Convention |g 67 -- |g Chapter 1 |t Spaces of Nilpotent Orbits and Spaces of Nilpotent i-Orbits |g 70 -- |g 1.1 |t Hodge Structures and Polarized Hodge Structures |g 70 -- |g 1.2 |t Classifying Spaces of Hodge Structures |g 71 -- |g 1.3 |t Extended Classifying Spaces |g 72 -- |g Chapter 2 |t Logarithmic Hodge Structures |g 75 -- |g 2.1 |t Logarithmic Structures |g 75 -- |g 2.2 |t Ringed Spaces (X[superscript log], O[subscript X superscript log]) |g 81 -- |g 2.3 |t Local Systems on X[superscript log] |g 88 -- |g 2.4 |t Polarized Logarithmic Hodge Structures |g 94 -- |g 2.5 |t Nilpotent Orbits and Period Maps |g 97 -- |g 2.6 |t Logarithmic Mixed Hodge Structures |g 105 -- |g Chapter 3 |t Strong Topology and Logarithmic Manifolds |g 107 -- |g 3.1 |t Strong Topology |g 107 -- |g 3.2 |t Generalizations of Analytic Spaces |g 115 -- |g 3.3 |t Sets E[subscript sigma] and E[subscript sigma superscript sharp] |g 120 -- |g 3.4 |t Spaces E[subscript sigma], [Gamma]/D[subscript Sigma], E[subscript sigma superscript sharp], and D[subscript Sigma superscript sharp] |g 125 -- |g 3.5 |t Infinitesimal Calculus and Logarithmic Manifolds |g 127 -- |g 3.6 |t Logarithmic Modifications |g 133 -- |g Chapter 4 |t Main Results |g 146 -- |g 4.1 |t Theorem A: The Spaces E[subscript sigma], [Gamma]/D[subscript Sigma], and [Gamma]/D[subscript Sigma sharp] |g 146 -- |g 4.2 |t Theorem B: The Functor PLH[subscript phi] |g 147 -- |g 4.3 |t Extensions of Period Maps |g 148 -- |g 4.4 |t Infinitesimal Period Maps |g 153 -- |g Chapter 5 |t Fundamental Diagram |g 157 -- |g 5.1 |t Borel-Serre Spaces (Review) |g 158 -- |g 5.2 |t Spaces of SL(2)-Orbits (Review) |g 165 -- |g 5.3 |t Spaces of Valuative Nilpotent Orbits |g 170 -- |g 5.4 |t Valuative Nilpotent i-Orbits and SL(2)-Orbits |g 173 -- |g Chapter 6 |t The Map [psi] : D[subscript val superscript sharp] to D[subscript SL] (2) |g 175 -- |g 6.1 |t Review of [CKS] and Some Related Results |g 175 -- |g 6.2 |t Proof of Theorem 5.4.2 |g 186 -- |g 6.3 |t Proof of Theorem 5.4.3 (i) |g 190 -- |g 6.4 |t Proofs of Theorem 5.4.3 (ii) and Theorem 5.4.4 |g 195 -- |g Chapter 7 |t Proof of Theorem A |g 205 -- |g 7.1 |t Proof of Theorem A (i) |g 205 -- |g 7.2 |t Action of [sigma subscript C] on E[subscript sigma] |g 209 -- |g 7.3 |t Proof of Theorem A for [Gamma]([sigma])[superscript gp]/D[subscript sigma] |g 215 -- |g 7.4 |t Proof of Theorem A for [Gamma]/D[subscript Sigma] |g 220 -- |g Chapter 8 |t Proof of Theorem B |g 226 -- |g 8.1 |t Logarithmic Local Systems |g 226 -- |g 8.2 |t Proof of Theorem B |g 229 -- |g 8.3 |t Relationship among Categories of Generalized Analytic Spaces |g 235 -- |g 8.4 |t Proof of Theorem 0.5.29 |g 241 -- |g Chapter 9 |t [flat]-Spaces |g 244 -- |g 9.1 |t Definitions and Main Properties |g 244 -- |g 9.2 |t 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] |g 246 -- |g 9.3 |t Proof of Theorem 9.1.4 for [Gamma]/D[subscript SL(2), less than or equal 1 superscript flat] |g 248 -- |g 9.4 |t Extended Period Maps |g 249 -- |g Chapter 10 |t Local Structures of D[subscript SL(2)] and [Gamma]/D[subscript SL(2), less than or equal 1 superscript flat] |g 251 -- |g 10.1 |t Local Structures of D[subscript SL(2)] |g 251 -- |g 10.2 |t A Special Open Neighborhood U(p) |g 255 -- |g 10.3 |t Proof of Theorem 10.1.3 |g 263 -- |g 10.4 |t 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] |g 269 -- |g Chapter 11 |t Moduli of PLH with Coefficients |g 271 -- |g 11.1 |t Space [Gamma]/D[subscript Sigma superscript A] |g 271 -- |g 11.2 |t PLH with Coefficients |g 274 -- |g 11.3 |t Moduli |g 275 -- |g Chapter 12 |t Examples and Problems |g 277 -- |g 12.1 |t Siegel Upper Half Spaces |g 277 -- |g 12.2 |t Case G[subscript R] [bsime] O(1, n -- 1, R) |g 281 -- |g 12.3 |t Example of Weight 3 (A) |g 290 -- |g 12.4 |t Example of Weight 3 (B) |g 295 -- |g 12.5 |t Relationship with [U2] |g 299 -- |g 12.6 |t Complete Fans |g 301 -- |g 12.7 |t Problems |g 304 -- |g A1 |t Positive Direction of Local Monodromy |g 307 -- |g A2 |t Proper Base Change Theorem for Topological Spaces |g 310. |
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| 546 | |a English. | ||
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| 650 | 0 | |a Hodge theory. | |
| 650 | 0 | |a Logarithms. | |
| 700 | 1 | |a Usui, Sampei. | |
| 730 | 0 | |a WORLDSHARE SUB RECORDS | |
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| 830 | 0 | |a Annals of mathematics studies ; |v no. 169. | |
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