Hodge ideals

Mircea Mustaţă; Mihnea Popa

doi:10.1090/MEMO/1268

Hodge ideals

Mircea Mustaţă, Mihnea Popa

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1-92
Number of pages	92
Journal	Memoirs of the American Mathematical Society
Volume	262
Issue number	1268
DOIs	https://doi.org/10.1090/MEMO/1268
State	Published - 2019

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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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.",

author = "Mircea Musta{\c t}{\u a} and Mihnea Popa",

note = "Funding Information: MM was partially supported by NSF grants DMS-1401227 and DMS-1265256; MP was partially supported by NSF grant DMS-1405516 and a Simons Fellowship. Publisher Copyright: {\textcopyright} 2019 American Mathematical Society",

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AU - Popa, Mihnea

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Y1 - 2019

N2 - 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.

AB - 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.

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Hodge ideals

Abstract

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