# Permutations on Weierstrass Prym eigenforms

@inproceedings{GutierrezRomo2021PermutationsOW, title={Permutations on Weierstrass Prym eigenforms}, author={Rodolfo Guti'errez-Romo and Angel Pardo}, year={2021} }

Let X ∈ H(2) be a Veech surface of discriminant D and let G (X) be the permutation group induced by the a ne group of X on the set of Weierstrass points of X . We show thatG (X) Dih4 if D≡4 0,G (X) Dih5 if D≡8 5, andG (X) Dih6 if D≡81, whereDihn is the dihedral group of order 2n. Thus,G (X) is a weak invariant, as it can distinguish the residue class ofDmod 8, but it cannot tell di erent spin invariants apart whenD≡81. Moreover, we show that the same groups arise whenwe only consider the action…

## Figures from this paper

## References

SHOWING 1-10 OF 13 REFERENCES

Teichmüller curves generated by Weierstrass Prym eigenforms in genus 3 and genus 4

- Mathematics
- 2014

This paper is devoted to the classification of the infinite families of Teichmüller curves generated by Prym eigenforms in genus 3 (and partially in genus 4) having a single zero (previously…

The number of genus 2 covers of an elliptic curve

- Mathematics
- 2006

The main aim of this paper is to determine the number cN,D of genus 2 covers of an elliptic curve E of fixed degree N ≥ 1 and fixed discriminant divisor D ∈Div (E). In the case that D is reduced,…

Prime arithmetic Teichmuller discs in H(2)

- Mathematics
- 2004

It is well-known that Teichmuller discs that pass through "integer points'' of the moduli space of abelian differentials are very special: they are closed complex geodesics. However, the structure of…

Flat Surfaces

- Mathematics
- 2006

Various problems of geometry, topology and dynamical systems on surfaces as well as some questions concerning one-dimensional dynamical systems lead to the study of closed surfaces endowed with a…

Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards

- Mathematics
- 1989

There exists a Teichmuller discΔ n containing the Riemann surface ofy2+x n =1, in the genus [n−1/2] Teichmuller space, such that the stabilizer ofΔ n in the mapping class group has a fundamental…

WEIERSTRASS PRYM EIGENFORMS IN GENUS FOUR

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2019

We prove the connectedness of the Prym eigenforms loci in genus four (for real multiplication by some order of discriminant $D$), for any $D$. These loci were discovered by McMullen in 2006.

Geometric Realizations of Hyperelliptic Curves

- Mathematics
- 1995

Every elliptic curve w 2 - z(z - 1)(z - y) = 0,y ≠ 0, 1 is a torus and, in particular, can be represented as an identification space of a parallelogram. The gluing maps are translations.

A Non-varying Phenomenon with an Application to the Wind-Tree Model

- MathematicsInternational Mathematics Research Notices
- 2018

We exhibit a non-varying phenomenon for the counting problem of cylinders, weighted by their area, passing through two marked (regular) Weierstrass points of a translation surface in a…

Dynamics of SL 2 ( R ) over moduli space in genus two

- Mathematics
- 2003

This paper classifies orbit closures and invariant measures for the natural action of SL2(R) on ΩM2, the bundle of holomorphic 1-forms over the moduli space of Riemann surfaces of genus two.

Prym Varieties and Teichmüller Curves

- Mathematics
- 2006

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