Duke Mathematical Journal

Arithmetic Veech sublattices of SL(2,Z)

Jordan S. Ellenberg and D. B. McReynolds

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Abstract

We prove that every algebraic curve X/Q¯ is birational over C to a Teichmüller curve. This result is a corollary of our main theorem, which asserts that most finite-index subgroups of SL(2,Z) are Veech groups.

Article information

Source
Duke Math. J., Volume 161, Number 3 (2012), 415-429.

Dates
First available in Project Euclid: 1 February 2012

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1328105285

Digital Object Identifier
doi:10.1215/00127094-1507412

Mathematical Reviews number (MathSciNet)
MR2180399

Zentralblatt MATH identifier
1244.32009

Subjects
Primary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Secondary: 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)

Citation

Ellenberg, Jordan S.; McReynolds, D. B. Arithmetic Veech sublattices of $\operatorname{SL}(2,\mathbf{Z})$. Duke Math. J. 161 (2012), no. 3, 415--429. doi:10.1215/00127094-1507412. https://projecteuclid.org/euclid.dmj/1328105285


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