Hodge filtration, minimal exponent, and local vanishing

Mircea Mustaţă; Mihnea Popa

doi:10.1007/s00222-019-00933-x

Hodge filtration, minimal exponent, and local vanishing

Mircea Mustaţă, Mihnea Popa^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English (US)
Pages (from-to)	453-478
Number of pages	26
Journal	Inventiones Mathematicae
Volume	220
Issue number	2
DOIs	https://doi.org/10.1007/s00222-019-00933-x
State	Published - May 1 2020

ASJC Scopus subject areas

Mathematics(all)

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AB - 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.

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Hodge filtration, minimal exponent, and local vanishing

Abstract

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