an:06098924
Zbl 1253.14036
Li, Si; Lian, Bong H.; Yau, Shing-Tung
Picard-Fuchs equations for relative periods and Abel-Jacobi map for Calabi-Yau hypersurfaces
EN
Am. J. Math. 134, No. 5, 1345-1384 (2012).
00308830
2012
j
14J32 14C30 14D05 33C50 81T30
Picard-Fuchs equations; Abel-Jacobi map; GKZ-hypergeometric; branes; Calabi-Yau
The authors aim to provide further development on the mathematical structures underlying inhomogeneous Picard-Fuchs equations and Abel-Jacobi maps.
More explicitly, they study the variation of relative cohomology for a pair consisting of a smooth projective hypersurface and an algebraic subvariety in it. Among other things, using the variation formalism, the authors prove that the relative periods of toric B-branes on Calabi-Yau hypersurface satisfy the enhanced GKZ hypergeometric system proposed in physics literature. The solution to the enhanced hypergeometric system is also provided.
Vehbi Emrah Paksoy (Fort Lauderdale)