Study of the topological string theory

2014 Fiscal Year Final Research Report

• Project/Area Number: 22740013
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: KONISHI Yukiko 京都大学, 理学(系)研究科(研究院), 准教授 (30505649)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: ミラー対称性 / フロベニウス多様体 / 量子コホモロジー / 混合ホッジ構造

Outline of Final Research Achievements

The objectives of the research are the generalization of the notion of Frobenius structure and the formulation of local mirror symmetry. Noticing that the B-model of the local mirror symmetry is described in terms of the mixed Hodge structure whereas that of the mirror symmetry is described in terms of the pure Hodge structure, we generalized the definition of Frobenius structure to the case where the tangent bundle has a filtration and named it the mixed Frobenius structure(MFS). Moreover we constructed a MFS for local A-model. More precisely, for a pair of a nonsingular projective variety and a concave vector bundle, we constructed a MFS by considering the nonequivariant limit of the twisted equivariant quantum cohomology and twisted pairing. These results are obtained in a joint work with Satoshi Minabe.

Free Research Field

代数幾何学・数理物理