Hodge filtration, minimal exponent, and local vanishing
Algebraic Geometry
2020-04-22 v2
Abstract
We bound the generation level of the Hodge filtration on the localization along a hypersurface in terms of its minimal exponent. As a consequence, we obtain a local vanishing theorem for sheaves of forms with log poles. These results are extended to Q-divisors, and are derived from a result of independent interest on the generation level of the Hodge filtration on nearby and vanishing cycles.
Cite
@article{arxiv.1901.05780,
title = {Hodge filtration, minimal exponent, and local vanishing},
author = {Mircea Mustata and Mihnea Popa},
journal= {arXiv preprint arXiv:1901.05780},
year = {2020}
}
Comments
19 pages; v. 2: revised version (including change in convention regarding the shift of Hodge filtrations under left-right equivalence), to appear in Invent. Math