English

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

Algebraic Geometry 2020-03-31 v5

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.

Keywords

Cite

@article{arxiv.1807.01935,
  title  = {Hodge ideals for Q-divisors, V-filtration, and minimal exponent},
  author = {Mircea Mustata and Mihnea Popa},
  journal= {arXiv preprint arXiv:1807.01935},
  year   = {2020}
}

Comments

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