Hodge ideals for-divisors,-filtration, and minimal exponent

Mircea Mustata; Mihnea Popa

doi:10.1017/fms.2020.18

Hodge ideals for-divisors,-filtration, and minimal exponent

Mircea Mustata, Mihnea Popa

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

1 Scopus citations

Abstract

We compute the Hodge ideals of-divisors in terms of the-filtration induced by a local defining equation, inspired by a result of Saito in the reduced case. We deduce basic properties of Hodge ideals in this generality, and relate them to Bernstein-Sato polynomials. As a consequence of our study we establish general properties of the minimal exponent, a refined version of the log canonical threshold, and bound it in terms of discrepancies on log resolutions, addressing a question of Lichtin and Kollár.

Original language	English (US)
Article number	18
Journal	Forum of Mathematics, Sigma
Volume	8
DOIs	https://doi.org/10.1017/fms.2020.18
State	Published - 2020

Keywords

2010 Mathematics Subject Classification: 14F10 14J17 32S25 14D07

ASJC Scopus subject areas

Analysis
Theoretical Computer Science
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Mathematics

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title = "Hodge ideals for-divisors,-filtration, and minimal exponent",

abstract = "We compute the Hodge ideals of-divisors in terms of the-filtration induced by a local defining equation, inspired by a result of Saito in the reduced case. We deduce basic properties of Hodge ideals in this generality, and relate them to Bernstein-Sato polynomials. As a consequence of our study we establish general properties of the minimal exponent, a refined version of the log canonical threshold, and bound it in terms of discrepancies on log resolutions, addressing a question of Lichtin and Koll{\'a}r. ",

keywords = "2010 Mathematics Subject Classification: 14F10 14J17 32S25 14D07",

author = "Mircea Mustata and Mihnea Popa",

note = "Funding Information: We are grateful to Morihiko Saito for comments and suggestions that helped improve a previous version of this paper. We would also like to thank Nero Budur and Mingyi Zhang for a few useful discussions, and a referee for several corrections. MM was partially supported by NSF grant DMS-1701622 and a Simons Fellowship; MP was partially supported by NSF grant DMS-1700819.",

year = "2020",

doi = "10.1017/fms.2020.18",

language = "English (US)",

volume = "8",

journal = "Forum of Mathematics, Sigma",

issn = "2050-5094",

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T1 - Hodge ideals for-divisors,-filtration, and minimal exponent

AU - Mustata, Mircea

AU - Popa, Mihnea

N1 - Funding Information: We are grateful to Morihiko Saito for comments and suggestions that helped improve a previous version of this paper. We would also like to thank Nero Budur and Mingyi Zhang for a few useful discussions, and a referee for several corrections. MM was partially supported by NSF grant DMS-1701622 and a Simons Fellowship; MP was partially supported by NSF grant DMS-1700819.

PY - 2020

Y1 - 2020

N2 - We compute the Hodge ideals of-divisors in terms of the-filtration induced by a local defining equation, inspired by a result of Saito in the reduced case. We deduce basic properties of Hodge ideals in this generality, and relate them to Bernstein-Sato polynomials. As a consequence of our study we establish general properties of the minimal exponent, a refined version of the log canonical threshold, and bound it in terms of discrepancies on log resolutions, addressing a question of Lichtin and Kollár.

AB - We compute the Hodge ideals of-divisors in terms of the-filtration induced by a local defining equation, inspired by a result of Saito in the reduced case. We deduce basic properties of Hodge ideals in this generality, and relate them to Bernstein-Sato polynomials. As a consequence of our study we establish general properties of the minimal exponent, a refined version of the log canonical threshold, and bound it in terms of discrepancies on log resolutions, addressing a question of Lichtin and Kollár.

KW - 2010 Mathematics Subject Classification: 14F10 14J17 32S25 14D07

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DO - 10.1017/fms.2020.18

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SN - 2050-5094

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Hodge ideals for-divisors,-filtration, and minimal exponent

Abstract

Keywords

ASJC Scopus subject areas

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