2014年3月
Some Remarks on the Semipositivity Theorems
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES
- ,
- ,
- 巻
- 50
- 号
- 1
- 開始ページ
- 85
- 終了ページ
- 112
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.4171/PRIMS/125
- 出版者・発行元
- KYOTO UNIV, PUBLICATIONS RESEARCH INST MATHEMATICAL SCIENCES
We show that the dualizing sheaves of reduced simple normal crossings pairs have a canonical weight filtration 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.
- リンク情報
- ID情報
-
- DOI : 10.4171/PRIMS/125
- ISSN : 0034-5318
- Web of Science ID : WOS:000335081900003