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arXiv · 1807.01935

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

Mircea Mustata·Mihnea Popa
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Abstract

We explicitly compute the Hodge ideals of 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 Koll\'ar.

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Mircea Mustata, Mihnea Popa. 2018-07-05. Hodge ideals for Q-divisors, V-filtration, and minimal exponent. https://arxiv.org/abs/1807.01935

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