Families of K3 surfaces and Lyapunov exponents
Abstract
Consider a family of K3 surfaces over a hyperbolic curve (i.e. Riemann surface). Their second cohomology groups form a local system, and we show that its top Lyapunov exponent is a rational number. One proof uses the KugaSatake construction, which reduces the question to Hodge structures of weight 1. A second proof uses integration by parts. The case of maximal Lyapunov exponent corresponds to modular families, given by the Kummer construction on a product of isogenous elliptic curves.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.1779
 Bibcode:
 2014arXiv1412.1779F
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Algebraic Geometry;
 Mathematics  Geometric Topology
 EPrint:
 35 pages, 1 figure