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Families Of K3 surfaces and Lyapunov exponents

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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 Kuga–Satake 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 coming from the Kummer construction.

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  1. Department of Mathematics, Harvard University, 1 Oxford St, Cambridge, MA, 02139, USA

    Simion Filip

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Filip, S. Families Of K3 surfaces and Lyapunov exponents. Isr. J. Math. 226, 29–69 (2018). https://doi.org/10.1007/s11856-018-1682-4

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  • DOI: https://doi.org/10.1007/s11856-018-1682-4

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