GL^+(2,R)-orbits in Prym eigenform loci
Abstract
This paper is devoted to the classification of GL^+(2,R)-orbit closures of surfaces in the intersection of the Prym eigenform locus with various strata of quadratic differentials. We show that the following dichotomy holds: an orbit is either closed or dense in a connected component of the Prym eigenform locus. The proof uses several topological properties of Prym eigenforms, which are proved by the authors in a previous work. In particular the tools and the proof are independent of the recent results of Eskin-Mirzakhani-Mohammadi. As an application we obtain a finiteness result for the number of closed GL^+(2,R)-orbits (not necessarily primitive) in the Prym eigenform locus Prym_D(2,2) for any fixed D that is not a square.
Cite
@article{arxiv.1310.8537,
title = {GL^+(2,R)-orbits in Prym eigenform loci},
author = {Erwan Lanneau and Duc-Manh Nguyen},
journal= {arXiv preprint arXiv:1310.8537},
year = {2016}
}
Comments
48 pages, 10 figures, Typos and part of proof rewritten