Periods of Limiting Mixed Hodge Structures of Projective Hypersurfaces

TL;DR

This paper demonstrates that for generic degenerations of projective hypersurfaces, the limiting mixed Hodge structure's periods are generated by special values of classical transcendental functions, using GKZ system analysis.

Contribution

It establishes a link between the periods of limiting mixed Hodge structures and special values of logarithm, Gamma, and Dirichlet L-functions, via GKZ system analytic continuation.

Findings

Periods are generated by special function values.

Analytic continuation of GKZ solutions is key.

Results connect Hodge theory with number theory.

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.