Hodge Ideals
We use methods from birational geometry to study the Hodge filtration on the localization along a hypersurface. This filtration leads to a sequence of ideal sheaves, called Hodge ideals, the first of which is a multiplier ideal. We analyze their local and global properties, and use them for applicat...
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| Hauptverfasser: | , |
|---|---|
| Format: | E-Book Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
2019
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| Ausgabe: | 1 |
| Schriftenreihe: | Memoirs of the American Mathematical Society |
| Schlagworte: | |
| ISBN: | 1470437813, 9781470437817 |
| ISSN: | 0065-9266, 1947-6221 |
| Online-Zugang: | Volltext |
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Inhaltsangabe:
- Introduction -- Preliminaries -- Saito’s Hodge filtration and Hodge modules -- Birational definition of Hodge ideals -- Basic properties of Hodge ideals -- Local study of Hodge ideals -- Vanishing theorems -- Vanishing on <inline-formula content-type="math/mathml"> P n {\mathbf P}^n </inline-formula> and abelian varieties,with applications -- Appendix: Higher direct imagesof forms with log poles -- References
- Cover -- Title page -- Chapter A. Introduction -- Chapter B. Preliminaries -- 1. Background on filtered \Dmod-modules -- 2. Localization along a divisor -- 3. Filtrations on localizations and tensor products -- Chapter C. Saito's Hodge filtration and Hodge modules -- 4. Hodge \Dmod-modules and strictness -- 5. Vanishing theorem -- 6. Localization as a Hodge \Dmod-module -- 7. Hodge filtration on the complement -- Chapter D. Birational definition of Hodge ideals -- 8. The simple normal crossing case -- 9. The general case -- 10. The case =0. -- 11. Independence of resolution, and filtration property -- 12. Comparison with Hodge filtration, and strictness property -- 13. Chain of inclusions -- Chapter E. Basic properties of Hodge ideals -- 14. The ideals _{ }( ). -- 15. Behavior under smooth pullback -- 16. Restriction to hypersurfaces -- 17. Generation level of the Hodge filtration -- 18. Behavior with respect to birational morphisms -- Chapter F. Local study of Hodge ideals -- 19. Order of vanishing along exceptional divisors -- 20. Examples -- 21. Order of vanishing along a closed subset -- Chapter G. Vanishing theorems -- 22. General vanishing -- 23. Vanishing for Hodge ideals -- 24. Effective version -- Chapter H. Vanishing on \PPⁿ and abelian varieties,with applications -- 25. Vanishing on \PPⁿ and toric varieties -- 26. Bounds for the subschemes associated to Hodge ideals in \PPⁿ -- 27. Singular points on hypersurfaces in \PPⁿ -- 28. Vanishing on abelian varieties -- 29. Singularities of theta divisors -- 30. Singular points on ample divisors on abelian varieties -- Appendix: Higher direct imagesof forms with log poles -- 1. The case of SNC divisors on the base -- 2. Akizuki-Nakano-type vanishing theorems -- References -- Back Cover