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Hodge Ideals
About this Title
Mircea Mustaţă, Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109 and Mihnea Popa, Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
Publication: Memoirs of the American Mathematical Society
Publication Year:
2019; Volume 262, Number 1268
ISBNs: 978-1-4704-3781-7 (print); 978-1-4704-5509-5 (online)
DOI: https://doi.org/10.1090/memo/1268
Published electronically: December 18, 2019
MSC: Primary 14J17, 32S25, 14D07, 14F17
Table of Contents
Chapters
- 1. Introduction
- 2. Preliminaries
- 3. Saito’s Hodge filtration and Hodge modules
- 4. Birational definition of Hodge ideals
- 5. Basic properties of Hodge ideals
- 6. Local study of Hodge ideals
- 7. Vanishing theorems
- 8. Vanishing on ${\mathbf P}^n$ and abelian varieties,with applications
- Appendix: Higher direct imagesof forms with log poles
- References
Abstract
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.- Peter Brückmann and Patrick Winkert, $T$-symmetrical tensor differential forms with logarithmic poles along a hypersurface section, Int. J. Pure Appl. Math. 46 (2008), no. 1, 111–136. MR 2433720
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