Hodge filtration, minimal exponent, and local vanishing

  • Mircea Mustaţă
  • Mihnea PopaEmail author


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 \({\mathbf {Q}}\)-divisors, and are derived from a result of independent interest on the generation level of the Hodge filtration on nearby and vanishing cycles.

Mathematics Subject Classification

14F10 14F17 14J17 32S25 



We thank the referee for very useful comments that helped us improve the exposition.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsNorthwestern UniversityEvanstonUSA

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