Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmueller curve

Details Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmueller curve Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmueller curve

2004-10-11

arxiv.org/abs/math/0410262v2

Mathematics

Algebraic Geometry

13 pages, Thm. 2.5 (now Thm 2.6) corrected and improved

Scientific paper

Periodic points are points on Veech surfaces, whose orbit under the group of affine diffeomorphisms is finite. We characterise those points as being torsion points if the Veech surfaces is suitably mapped to its Jacobian or an appropriate factor thereof. For a primitive Veech surface in genus two we show that the only periodic points are the Weierstrass points and the singularities. Our main tool is the Hodge-theoretic characterisation of Teichmueller curves. We deduce from it a finiteness result for the Mordell-Weil group of the family of Jacobians over a Teichmueller curve.

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