Hodge ideals for Q-divisors: Birational approach

Mircea Mustatǎ; Mihnea Popa

doi:10.5802/jep.94

Hodge ideals for Q-divisors: Birational approach

Mircea Mustatǎ, Mihnea Popa

Mathematics PhD Program

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

5 Scopus citations

Abstract

We develop the theory of Hodge ideals for Q-divisors by means of log resolutions, extending our previous work on reduced hypersurfaces. We prove local (non-)triviality criteria and a global vanishing theorem, as well as other analogues of standard results from the theory of multiplier ideals, and we derive a new local vanishing theorem. The connection with the V -filtration is analyzed in a sequel.

Original language	English (US)
Pages (from-to)	283-328
Number of pages	46
Journal	Journal de l'Ecole Polytechnique - Mathematiques
Volume	6
DOIs	https://doi.org/10.5802/jep.94
State	Published - 2019

Keywords

D-modules
Hodge filtration
Hodge ideals
Minimal exponent
Vanishing theorems

ASJC Scopus subject areas

Mathematics(all)

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10.5802/jep.94

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abstract = "We develop the theory of Hodge ideals for Q-divisors by means of log resolutions, extending our previous work on reduced hypersurfaces. We prove local (non-)triviality criteria and a global vanishing theorem, as well as other analogues of standard results from the theory of multiplier ideals, and we derive a new local vanishing theorem. The connection with the V -filtration is analyzed in a sequel.",

keywords = "D-modules, Hodge filtration, Hodge ideals, Minimal exponent, Vanishing theorems",

author = "Mircea Mustatǎ and Mihnea Popa",

note = "Funding Information: MM was partially supported by NSF grant DMS-1701622; MP was partially supported by NSF grant DMS-1700819. Publisher Copyright: {\textcopyright} Les auteurs, 2019. Certains droits r{\'e}serv{\'e}s.",

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doi = "10.5802/jep.94",

language = "English (US)",

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T1 - Hodge ideals for Q-divisors

T2 - Birational approach

AU - Mustatǎ, Mircea

AU - Popa, Mihnea

N1 - Funding Information: MM was partially supported by NSF grant DMS-1701622; MP was partially supported by NSF grant DMS-1700819. Publisher Copyright: © Les auteurs, 2019. Certains droits réservés.

PY - 2019

Y1 - 2019

N2 - We develop the theory of Hodge ideals for Q-divisors by means of log resolutions, extending our previous work on reduced hypersurfaces. We prove local (non-)triviality criteria and a global vanishing theorem, as well as other analogues of standard results from the theory of multiplier ideals, and we derive a new local vanishing theorem. The connection with the V -filtration is analyzed in a sequel.

AB - We develop the theory of Hodge ideals for Q-divisors by means of log resolutions, extending our previous work on reduced hypersurfaces. We prove local (non-)triviality criteria and a global vanishing theorem, as well as other analogues of standard results from the theory of multiplier ideals, and we derive a new local vanishing theorem. The connection with the V -filtration is analyzed in a sequel.

KW - D-modules

KW - Hodge filtration

KW - Hodge ideals

KW - Minimal exponent

KW - Vanishing theorems

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M3 - Article

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VL - 6

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EP - 328

JO - Journal de l'Ecole Polytechnique - Mathematiques

JF - Journal de l'Ecole Polytechnique - Mathematiques

SN - 2429-7100

ER -

Hodge ideals for Q-divisors: Birational approach

Abstract

Keywords

ASJC Scopus subject areas

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