Periods of Limiting Mixed Hodge Structures of Projective Hypersurfaces

Abstract

For a generic one-parameter degeneration of projective hypersurfaces, we show that the periods of the limiting mixed Hodge structure are generated by certain special values of logarithm, Gamma and Dirichlet $L$-functions. Our proof is based on the analytic continuation of solutions to the GKZ system.

46 pages, comments are welcome