Geometry of Picard varieties of degenerate varietiesvia log structures
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 |
|
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.
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Report
(4 results)
Research Products
(3 results)