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ON ARITHMETIC CURVES IN THE MODULI SPACES OF CURVES

Published online by Cambridge University Press:  15 April 2005

Pierre Lochak
Pierre Lochak
Affiliation:
Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, F-75013 Paris, France (lochak@math.jussieu.fr)
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Abstract

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We study several types of curves and higher-dimensional objects inside the moduli spaces of curves, insisting on their arithmetic properties in the perspective of Grothendieck–Teichmüller theory. On the way we explicitly identify those curves which were originally associated by W. Veech with certain rational polygonal billiards.

AMS 2000 Mathematics subject classification: Primary 14D22; 32G15; 14H30

Keywords

moduli spaces of curvesGrothendieck–Teichmüller theoryrational polygonal billiards
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 4 , Issue 3 , July 2005 , pp. 443 - 508
Copyright
2005 Cambridge University Press