2010 Fiscal Year Final Research Report

Mixed Hodge structures on log smooth degenerations

Research Project

Project/Area Number	20540054
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Algebra
Research Institution	Tokyo Denki University
Principal Investigator	FUJISAWA Taro Tokyo Denki University, 工学部, 准教授 (60280385)
Project Period (FY)	2008 – 2010
Keywords	混合ホッジ構造 / 対数構造
Research Abstract	I succeeded to construct "product" and "the trace map" on the relative log de Rham cohomology groups of a log deformation, which is a typical example of log smooth degeneration. Moreover, I proved that these data provided a polarization on mixed Hodge structures, where the polarization is not a bilinear form on the graded pieces by the weight filtration on the log de Rham cohomology groups, but a bilinear form on the whole log de Rham cohomology groups satisfying the appropriated properties on the graded pieces by the weight filtration.

(3 results)