HODGE IDEALS FOR -DIVISORS, -FILTRATION, AND MINIMAL EXPONENT

Abstract

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.