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HODGE IDEALS FOR $\mathbb{Q}$-DIVISORS, $V$-FILTRATION, AND MINIMAL EXPONENT

Part of: Families, fibrations Surfaces and higher-dimensional varieties (Co)homology theory Singularities

Published online by Cambridge University Press:  17 April 2020

MIRCEA MUSTAŢĂ  and
MIHNEA POPA
MIRCEA MUSTAŢĂ
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA; mmustata@umich.edu
MIHNEA POPA
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, USA; mpopa@math.northwestern.edu

Abstract

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We compute the Hodge ideals of $\mathbb{Q}$-divisors in terms of the $V$-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.

MSC classification

Primary: 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 14J17: Singularities 32S25: Surface and hypersurface singularities 14D07: Variation of Hodge structures
Type
Algebraic and Complex Geometry
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e19
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2020

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