Finiteness Results for Teichmüller Curves

Hodge-teichmüller Planes and Finiteness Results for Teichmüller Curves

We prove that there are only finitely many algebraically primitive Teichmüller curves in the minimal stratum in each prime genus at least 3. The proof is based on the study of certain special planes in the first cohomology of a translation surface which we call Hodge-Teichmüller planes. We also show that algebraically primitive Teichmüller curves are not dense in any connected component of any ...

Periodic Points on Veech Surfaces and the Mordell-weil Group over a Teichmüller Curve

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 too...

Prym varieties and Teichmüller curves

This paper gives a uniform construction of infinitely many primitive Teichmüller curves V ⊂ Mg for g = 2, 3 and 4.

Teichmüller curves in genus two: Discriminant and spin

Teichmüller curves in genus two: Torsion divisors and ratios of sines