Billiards and Teichmüller curves on Hilbert modular surfaces

McMullen, Curtis

doi:10.1090/S0894-0347-03-00432-6

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Billiards and Teichmüller curves on Hilbert modular surfaces

Author: Curtis T. McMullen
Journal: J. Amer. Math. Soc. 16 (2003), 857-885
MSC (2000): Primary 32G15; Secondary 37D50, 11F41, 14G35
Posted: June 19, 2003
MathSciNet review: 1992827
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Abstract: This paper exhibits an infinite collection of algebraic curves isometrically embedded in the moduli space of Riemann surfaces of genus two. These Teichmüller curves lie on Hilbert modular surfaces parameterizing Abelian varieties with real multiplication. Explicit examples, constructed from L-shaped polygons, give billiard tables with optimal dynamical properties.

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