2011 Fiscal Year Final Research Report
Geometry of Picard varieties of degenerate varietiesvia log structures
| Project/Area Number |
21540032
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Yokohama National University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | 代数幾何 |
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| 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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