Families Of K3 surfaces and Lyapunov exponents |
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Authors: | Simion Filip |
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Institution: | 1.Department of Mathematics,Harvard University,Cambridge,USA |
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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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