Hodge filtration, minimal exponent, and local vanishing

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.

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

Cited by in corpus (4)

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