Affine mappings of translation surfaces: geometry and arithmetic

By E. Gutkin, C. Judge. 2000

240 citations recorded by the source corpus.

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Euler characteristics of Teichmüller curves in genus two (2006, background): “Arithmetic of Siegel–Veech constants According to [30], the Siegel–Veech constant c in (14–1) lies in the trace field of the Veech group of .”
An extraordinary origami curve (2005, methodology): “A more detailed introduction to translation surfaces and Veech groups can be found e.g. in [ GJ ] and [HuSc].”
Prym Varieties and Teichmüller Curves (2006, background): “In this case the groups SL(X, ωi), i = 1,2 are also commensurable (see e.g. [ GJ ]).”
Veech groups without parabolic elements (2005, methodology): “See also [ GuJu ] for a different approach of these notions.”
Grid graphs and lattice surfaces (2008, methodology): “If SL(X;!) is arithmetic, then (X;!) is a cover of a torus, branched at one point. See theorem 5 and [ GJ00 ].”
SQUARE-TILED CYCLIC COVERS (2010, background): “Its projection to the moduli space of curves is a Riemann surface with cusps, often called an arithmetic Teichmüller curve, see [35], [19].”
On groups generated by two positive multi-twists: Teichmuller curves and Lehmer's number (2003, background): “In particular, understanding and classifying Teichmüller curves and lattice polygons is an interesting problem which has received much attention (see eg Veech [56], [57], Harvey [27], Gutkin and Judge [25], Kenyon and Smillie [32], Puchta [48], McMullen [44], and Calta [13]).”