Central charges, symplectic forms, and hypergeometric series in local mirror symmetry

Abstract

We study a cohomology-valued hypergeometric series which naturally arises in the description of (local) mirror symmetry. We identify it as a central charge formula for BPS states and study its monodromy property from the viewpoint of Kontsevich's homological mirror symmetry. In the case of local mirror symmetry, we will identify a symplectic form, and will conjecture an integral and symplectic monodromy property of a relevant hypergeometric series of Gel'fand-Kapranov-Zelevinski type.

35 pages, AMSLatex; v2: typos corrected and minor corrections, v3: construction of cycles in Appendix A completed, v4: typos corrected, To appear in "Mirror Symmetry V", Proceedings of BIRS workshop on Calabi-Yau Varieties and Mirror Symmetry, December 6-11, 2003

References in corpus (1)

• Autoequivalences of derived categories on the minimal resolutions of $A_n$-singularities on surfaces

Cited by in corpus (1)

• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds