Genus two Veech surfaces arising from general quadratic differentials

Details Genus two Veech surfaces arising from general quadratic differentials Genus two Veech surfaces arising from general quadratic differentials

2005-04-09

arxiv.org/abs/math/0504180v1

Mathematics

Geometric Topology

19 pages

Scientific paper

We study Veech surfaces of genus 2 arising from quadratic differentials that are not squares of abelian differentials. We prove that all such surfaces of type (2,2) and (2,1,1) are arithmetic. In (1,1,1,1) case, we reduce the question to abelian differentials of type (2,2) on hyperelliptic genus 3 surfaces with singularities at Weierstrass points, and we give an example of a non-arithmetic Veech surface.

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