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

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 Kollár.

Final version (35 pages), to appear in Forum Math. Sigma

References in corpus (2)

• Hodge ideals and microlocal V-filtration
• Hodge filtration and Hodge ideals for $\mathbb{Q}$-divisors with weighted homogeneous isolated singularities

Cited by in corpus (8)

• Hodge filtration and Hodge ideals for $\mathbb{Q}$-divisors with weighted homogeneous isolated singularities
• Hodge ideals and minimal exponents of ideals
• Hodge ideals for Q-divisors: birational approach
• Combining Igusa's conjectures on exponential sums and monodromy with semi-continuity of the minimal exponent
• Hodge ideals of free divisors
• Hodge ideal and spectrum of weighted homogeneous isolated singularities
• Multiplier ideals of analytically irreducible plane curves
• Vanishing for Hodge ideals of $\mathbb{Q}$-divisors