Finiteness results for Teichmueller curves

Details Finiteness results for Teichmueller curves Finiteness results for Teichmueller curves

2005-09-04

arxiv.org/abs/math/0509079v1

Mathematics

Algebraic Geometry

Scientific paper

We show that for each genus there are only finitely many algebraically
primitive Teichmueller curves C, such that i) C lies in the hyperelliptic locus
and ii) C is generated by an abelian differential with two zeros of order g-1.
We prove moreover that for these Teichmueller curves the trace field of the
affine group is not only totally real but cyclotomic.

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