We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
PICARD-FUCHS EQUATIONS FOR RELATIVE PERIODS AND ABEL-JACOBI MAP FOR CALABI-YAU HYPERSURFACES.
- Authors
SI LI; LIAN, BONG H.; SHING-TUNG YAU
- Abstract
We study the variation of relative cohomology for a pair consisting of a smooth projective hypersurface and an algebraic subvariety in it. We construct an inhomogeneous Picard-Fuchs equation by applying a Picard-Fuchs operator to the holomorphic top form on a Calabi-Yau hypersurface in toric variety, and deriving a general formula for the d-exact form on one side of the equation. We also derive a double residue formula, giving a purely algebraic way to compute the inhomogeneous Picard-Fuchs equations for the Abel-Jacobi map, which has played an important role in the recent study of D-branes (by Morrison and Walcher). Using the variation formalism, we prove that the relative periods of toric B-branes on Calabi-Yau hypersurface satisfy the enhanced GKZ-hypergeometric system proposed in physics literature (by Alim, Hecht, Mayr, and Mertens), and discuss the relations between several works in the recent study of open string mirror symmetry. We also give the general solutions to the enhanced hypergeometric system.
- Subjects
EQUATIONS; CALABI-Yau manifolds; HYPERSURFACES; ALGEBRAIC varieties; COHOMOLOGY theory; HOLOMORPHIC functions
- Publication
American Journal of Mathematics, 2012, Vol 134, Issue 5, p1345
- ISSN
0002-9327
- Publication type
Article
- DOI
10.1353/ajm.2012.0039