Universal periods of hyperelliptic curves and their applications

摘要

We construct universal power series for differential 1-forms and period integrals of Schottky-Mumford uniformized hyperelliptic curves over local fields. Using these universal 1-forms and periods, we characterize Siegel modular forms vanishing on the hyperelliptic Jacobian locus, and construct universal and p-adic solutions of the Korteweg-de Vries hierarchy. (C) 2001 Elsevier Science B.V. All rights reserved. [References: 23]