ON ARITHMETIC CURVES IN THE MODULI SPACES OF CURVES

By P. Lochak. Journal of the Institute of Mathematics of Jussieu, 2005

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How researchers see this paper

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Teichmuller curves, triangle groups, and Lyapunov exponents (2005, methodology): “This was shown by Lochak ([ Lo05 ], see also [McM04]).”
Teichmüller curves in genus two: Torsion divisors and ratios of sines (2006, unknown): “Moreover, by [Lo] the Teichmüller curve”
Braid groups and Hodge theory (2013, background): “As shown in [Lo1] (see also [Mc2, §5]), the point configurations arising in V are given explicitly by”
An extraordinary origami curve (2005, background): “Another topic of interest is the action of the absolute Galois group of the rationals on them as discussed in [ Lo ] and [M1].”
SQUARE-TILED CYCLIC COVERS (2010, background): “In other words, we get a square-tiled surface, see [10], [41] (also called an origami, [25], [32]; also called an arithmetic translation surface, see [19]).”
Teichmüller curves in genus two: The decagon and beyond (2005, unknown): “For additional background on Teichmüller curves, see [Th], [V1], [V2], [Vo], [Wa], [KS], [Pu], [GJ], [EO], [Lei] and [Lo].”
Variations of Hodge structures of a Teichmüller curve (2006, background): “Since they are Hurwitz spaces, they are known ([Lo03], [Mo03]) to be deﬁned over Q .”