Hodge ideals / Mircea Mustaţă, Mihnea Popa.

Format:

Book

Author/Creator:

Mustata, Mircea, 1971- author.

Popa, Mihnea, 1973- author.

Series:

Memoirs of the American Mathematical Society ; Number 1268.

Memoirs of the American Mathematical Society ; Number 1268

Language:

English

Subjects (All):

Hodge theory.

Physical Description:

1 online resource (v, 80 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2019]

Summary:

"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 applications related to the singularities and Hodge theory of hypersurfaces and their complements"-- Provided by publisher.

Contents:

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.

Notes:

Description based on print version record.

Includes bibliographical references.

ISBN:

1-4704-5509-9