2010 Fiscal Year Final Research Report
Study of Moduli of algebraic vector bundles
| Project/Area Number |
20740009
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
ABE Takeshi Kyoto University, 大学院・自然科学研究科, 准教授 (90362409)
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| Project Period (FY) |
2008 – 2010
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| Keywords | ベクトル束 / モジュライ |
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| Research Abstract |
I studied on the strange duality of generalized theta functions on moduli spaces of vector bundles. I described the behavior of the strange duality map for symplectic bundles as the base curve degenerates to a singular curve, and proved the strange duality conjecture for symplectic bundles. By considering quasi-bundles on a projective plane, I proved a special case of Le Potier's strange duality conjecture. I also computed the dimension of generalized theta functions on the moduli spaces of pure one-dimensional sheaves of degree four.
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