Some Remarks on the Semipositivity Theorems

Access this Article

Search this Article

Abstract

We show that the dualizing sheaves of reduced simple normal crossings pairs have a canonical weight ltration in a compatible way with the one on the corresponding mixed Hodge modules by calculating the extension classes between the dualizing sheaves of smooth varieties. Using the weight spectral sequence of mixed Hodge modules, we then reduce the semipositivity theorem for the higher direct images of dualizing sheaves to the smooth case where the assertion is well known. This may be used to simplify some constructions in a recent paper of Y. Kawamata. We also give a simple proof of the semipositivity theorem for admissible variations of mixed Hodge structure in [FF] by using the theories of Cattani, Kaplan, Schmid, Steenbrink, and Zucker. This generalizes Kawamata's classical result in the pure case.

Journal

  • Publications of the Research Institute for Mathematical Sciences

    Publications of the Research Institute for Mathematical Sciences 50(1), 85-112, 2014

    EMS Publishing House

Codes

  • NII Article ID (NAID)
    120005394742
  • NII NACSIS-CAT ID (NCID)
    AA00796798
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    0034-5318
  • Data Source
    IR 
Page Top