Log picard varieties and their applications

Research Project

Project/Area Number	24540035
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Research Field	Algebra
Research Institution	Yokohama National University
Principal Investigator	KAJIWARA Takeshi 横浜国立大学, 工学(系)研究科(研究院), 教授 (00250663)
Project Period (FY)	2012-04-01 – 2015-03-31
Project Status	Completed (Fiscal Year 2014)
Budget Amount *help	¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000) Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000) Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000) Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords	代数幾何 / 対数構造 / ピカール多様体 / 退化代数多様体 / 退化多様体
Outline of Final Research Achievements	Our research studies geometry of log abelian varieties, and as its application, log Picard varieties. We mainly show the following. We introduce the notion of weak log abelian varieties, and show that such varieties are of finite presentation. We also construct their proper models. We apply these results and have compactification of some degenerating Picard varieties. The research on log abelian varieties is a joint work with Kazuya Kato and Chikara Nakayama.