Geometry of Picard varieties of degenerate varietiesvia log structures

Research Project

Project/Area Number	21540032
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Algebra
Research Institution	Yokohama National University
Principal Investigator	KAJIWARA Takeshi 横浜国立大学, 工学研究院, 准教授 (00250663)
Project Period (FY)	2009 – 2011
Project Status	Completed (Fiscal Year 2011)
Budget Amount *help	¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000) Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000) Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000) Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords	代数幾何 / 対数構造 / ピカール多様体 / 退化多様体
Research Abstract	Our research studies log abelian varieties, and their applications, and also structures of valuation rings. We mainly show the following results. First, we give a formulation of logarithmic Picard varieties of degenerate varieties, by using the structures of logarithmic abelian varieties. Next, we construct the moduli spaces of logarithmic elliptic curves. This is a joint work with Kazuya Kato, and Chikara Nakayama. Finally, we prove properness of models of logarithmic abelian varieties associated to complete fans.

Report

(4 results)