# ORBIFOLD POINTS ON PRYM–TEICHMÜLLER CURVES IN GENUS $4$

@article{TorresTeigell2017ORBIFOLDPO, title={ORBIFOLD POINTS ON PRYM–TEICHM{\"U}LLER CURVES IN GENUS \$4\$}, author={David Torres-Teigell and Jonathan Zachhuber}, journal={Journal of the Institute of Mathematics of Jussieu}, year={2017}, volume={18}, pages={673 - 706} }

For each discriminant $D>1$ , McMullen constructed the Prym–Teichmüller curves $W_{D}(4)$ and $W_{D}(6)$ in ${\mathcal{M}}_{3}$ and ${\mathcal{M}}_{4}$ , which constitute one of the few known infinite families of geometrically primitive Teichmüller curves. In the present paper, we determine for each $D$ the number and type of orbifold points on $W_{D}(6)$ . These results, together with a previous result of the two authors in the genus $3$ case and with results of Lanneau–Nguyen and Möller…

## 5 Citations

ORBIFOLD POINTS ON PRYM-TEICHMÜLLER CURVES IN GENUS FOUR

- 2016

For each discriminant D > 1, McMullen constructed the PrymTeichmüller curves WD(4) and WD(6) in M3 and M4, which constitute one of the few known infinite families of geometrically primitive…

The Galois Action and a Spin Invariant for Prym-Teichm\"uller Curves in Genus 3

- Mathematics
- 2015

Given a Prym-Teichm\"uller curve in $\mathcal{M}_3$, this note provides an invariant that sorts the cusp prototypes of Lanneau and Nguyen by component. This can be seen as an analogue of McMullen's…

Non-Existence and Finiteness Results for Teichmüller Curves in Prym Loci

- MathematicsExperimental Mathematics
- 2019

The minimal stratum in Prym loci have been the first source of infinitely many primitive, but not algebraically primitive Teichmueller curves. We show that the stratum Prym(2,1,1) contains no such…

Billiards and Teichmüller curves

- 2021

A Teichmüller curve V ⊂ Mg is an isometrically immersed algebraic curve in the moduli space of Riemann surfaces. These rare, extremal objects are related to billiards in polygons, Hodge theory,…

Finiteness of Teichmüller Curves in Non-Arithmetic Rank 1 Orbit Closures

- Mathematics
- 2015

abstract:We show that in any non-arithmetic rank 1 orbit closure of translation surfaces, there are only finitely many Teichm\"uller curves. We also show that in any non-arithmetic rank 1 orbit…

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Given a Prym-Teichm\"uller curve in $\mathcal{M}_3$, this note provides an invariant that sorts the cusp prototypes of Lanneau and Nguyen by component. This can be seen as an analogue of McMullen's…

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