GL^+(2,R)-orbits in Prym eigenform loci

Erwan Lanneau; Duc-Manh Nguyen

doi:10.2140/gt.2016.20.1359

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arXiv · 1310.8537

GL^+(2,R)-orbits in Prym eigenform loci

Erwan Lanneau·Duc-Manh Nguyen

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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.

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BibTeX RIS

Erwan Lanneau, Duc-Manh Nguyen. 2014-03-18. GL^+(2,R)-orbits in Prym eigenform loci. https://doi.org/10.2140/gt.2016.20.1359

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