Billiards and Teichmüller Curves on Hilbert Modular Surfaces

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Billiards and Teichmüller Curves on Hilbert Modular Surfaces

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Title: Billiards and Teichmüller Curves on Hilbert Modular Surfaces
Author: McMullen, Curtis T.
Citation: McMullen, Curtis T. 2003. Billiards and Teichmüller curves on Hilbert modular surfaces. Journal of the American Mathematical Society 16: 857-885. Revised 2009.
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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.
Published Version: doi:10.1090/S0894-0347-03-00432-6
Other Sources: http://www.math.harvard.edu/~ctm/papers/index.html
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:3446007

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  • FAS Scholarly Articles [6466]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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