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GL^+(2,R)-orbits in Prym eigenform loci (1310.8537v2)

Published 31 Oct 2013 in math.GT and math.DS

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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