Study of Moduli of algebraic vector bundles

代数向量丛模的研究

• 批准号: 20740009
• 负责人: ABE Takeshi
• 金额: $ 2.25万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20740009/
• 关键词: ベクトル束; モジュライ

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.

研究了向量丛模空间上广义theta函数的奇异对偶性。描述了辛丛的奇对偶映射在基曲线退化为奇异曲线时的行为，证明了辛丛的奇对偶猜想。通过研究射影平面上的拟丛，证明了Le Potier奇异对偶猜想的一个特例。我还计算了四阶纯一维层模空间上广义theta函数的维数。

项目成果

Strange Duality for Parabolic Symplectic Bundles on a Pointed Projective Line

• DOI: 10.1093/imrn/rnn121
• 发表时间: 2010-07
• 期刊: International Mathematics Research Notices
• 影响因子: 1
• 作者: T. Abe

Projective normality of the moduli space of rank $2$ vector bundles on a generic curve.

通用曲线上秩 $2$ 向量束的模空间的投影正态性。

• 发表时间: 2010
• 期刊: Transactions of AMS 362
• 作者: 若槻聡;岡耕平;若槻聡;岡耕平;若槻聡;岡耕平;若槻聡;岡耕平;若槻聡;岡耕平;若槻聡;岡耕平;S. Wakatsuki;岡耕平;S.Wakatsuki;S. Wakatsuki;岡耕平;阿部健;Takeshi Abe
• 通讯作者: Takeshi Abe

Level-rank duality of conformal blocks of affirm symplectic Lie algebra and symplectic strange duality

肯定辛李代数共形块的级秩对偶性和辛奇异对偶性

• 发表时间: 2008
• 作者: H.Kawanoue;K.Matsuki;阿部健;Hiraku Kawanoue;Hiraku Kawanoue;阿部健;阿部健;阿部健;Hiraku Kawanoue;阿部健;阿部健;川ノ上帆;阿部健;川ノ上帆;川ノ上帆;阿部健;川ノ上帆;川ノ上帆;阿部健;川ノ上帆;阿部健;阿部健
• 通讯作者: 阿部健

Strange duality for symplectic bundles

辛丛的奇异对偶性

• 发表时间: 2008
• 作者: H.Kawanoue;K.Matsuki;阿部健;Hiraku Kawanoue;Hiraku Kawanoue;阿部健;阿部健;阿部健;Hiraku Kawanoue;阿部健;阿部健;川ノ上帆;阿部健;川ノ上帆;川ノ上帆;阿部健;川ノ上帆;川ノ上帆;阿部健;川ノ上帆;阿部健;阿部健;阿部健
• 通讯作者: 阿部健

Deformation of rank $2$ quasi-bundles and some strange dualities for rational surfaces

• DOI: 10.1215/00127094-2010-063
• 发表时间: 2010-12
• 期刊: Duke Mathematical Journal
• 影响因子: 2.5
• 作者: T. Abe