• Corpus ID: 244709641

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… 

References

SHOWING 1-10 OF 13 REFERENCES
Teichmüller curves generated by Weierstrass Prym eigenforms in genus 3 and genus 4
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
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)
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
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
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
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
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
  • Angel Pardo
  • Mathematics
    International 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
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
This paper gives a uniform construction of infinitely many primitive Teichmuller curves V ⊂ Mg for g = 2, 3 and 4.
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