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

By M. Mustaţă, Mihnea Cristian Popa. Forum of Mathematics, Sigma, 2018

55 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0e8a859ce79285a99e132b4c5b4c71fb42368a41