|Speaker:||Yukiko Konishi (Kyoto University)|
|Title:||Local B-model and mixed Hodge structure|
|Date (JST):||Mon, Nov 22, 2010, 14:00 - 17:00|
|Place:||Seminar Room A|
Given a two-dimensional reflexive polyhedron, we are able to construct:
(i) three-dimensional fan and the associated noncomplete toric variety;
(ii) Gelfand-Kapranov-Zelevinsky's hypergeometric system;
(iii) a family of Laurent polynomials whose Newton polyhedron is the given polyhedron
and thus a family of affine curves in two-dimensional algebraic torus.
The statement of the local mirror symmetry is that both
(i) (the genus zero local Gromov-Witten invariants of the toric variety;the local A-model)
and (iii)(the variation of mixed Hodge structures (VMHS) of the relative cohomology
of the affine curve and its ambient space;the local B-model) are governed by (ii).
I would like to talk about my joint work with Satoshi Minabe on a definition of the Yukawa coupling for the local B-model
[Local B-model and Mixed Hodge Structure, arXiv:0907.4108].
In Part I, I will explain the VMHS.
It has a description by a Jacobian ring due to Batyrev and Stienstra.
In Part II, I will give our definition of the Yukawa coupling.
If time permits, I would like to explain how to modify Bershadsky-Cecotti-Ooguri-Vafa's holomorphic anomaly equation to the local B-model.