Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-24T01:17:15.576Z Has data issue: false hasContentIssue false
  • English
  • Français

WEIERSTRASS PRYM EIGENFORMS IN GENUS FOUR

Part of: Dynamical systems with hyperbolic behavior Low-dimensional dynamical systems

Published online by Cambridge University Press:  14 February 2019

Erwan Lanneau  and
Duc-Manh Nguyen
Erwan Lanneau
Affiliation:
UMR CNRS 5582, Univ. Grenoble Alpes, CNRS, Institut Fourier, F-38000Grenoble, France ([email protected])
Duc-Manh Nguyen
Affiliation:
UMR CNRS 5251, IMB Bordeaux-Université de Bordeaux, 351, Cours de la Libération, 33405Talence Cedex, France ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

real multiplicationPrym locusTeichmüller curve

MSC classification

Primary: 37E05: Maps of the interval (piecewise continuous, continuous, smooth)
Secondary: 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 6 , November 2020 , pp. 2045 - 2085
Check for updates
Copyright
© Cambridge University Press 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Hubert, P. and Lelièvre, S., Prime arithmetic Teichmüller discs in H(2), Israel J. Math. 151 (2006), 281–321.Google Scholar
Lanneau, E. and Nguyen, D.-M., Teichmüller curves generated by Weierstrass Prym eigenforms in genus three and genus four, J. Topol. 7 (2) (2014), 475–522.Google Scholar
McMullen, C., Teichmüller curves in genus two: Discriminant and spin, Math. Ann. 333 (2005), 87–130.Google Scholar
McMullen, C., Prym varieties and Teichmüller curves, Duke Math. J. 133 (2006), 569–590.Google Scholar
Möller, M., Prym covers, theta functions and Kobayashi curves in Hilbert modular surfaces, Amer. J. Math. 136(4) (2014), 995–1021.Google Scholar
Torres, D. and Zachhuber, J., Orbifold Points on Prym-Teichmüller Curves in Genus Three, Int. Math. Res. Not. IMRN 2018(4) (2018), 1228–1280.Google Scholar
Torres, D. and Zachhuber, J., Orbifold Points on Prym-Teichmüller Curves in Genus Four, J. Inst. Math. Jussieu (2017), doi:10.1017/S1474748017000196.Google Scholar
Zachhuber, J., The Galois Action and a Spin Invariant for Prym-Teichmüller Curves in Genus 3, Bull. de la SMF. to appear, doi:10.24033/bsmf.2766.Google Scholar