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2016 $\mathrm{GL}^+(2,\mathbb{R})$–orbits in Prym eigenform loci
Erwan Lanneau, Duc-Manh Nguyen
Geom. Topol. 20(3): 1359-1426 (2016). DOI: 10.2140/gt.2016.20.1359


This paper is devoted to the classification of GL+(2, )–orbit closures of surfaces in the intersection of the Prym eigenform locus with various strata of abelian 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. In particular, the tools and the proof are independent of the recent results of Eskin and Mirzakhani and Eskin, Mirzakhani and Mohammadi.

As an application we obtain a finiteness result for the number of closed GL+(2, )–orbits (not necessarily primitive) in the Prym eigenform locus ΩED(2,2) for any fixed D that is not a square.


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Erwan Lanneau. Duc-Manh Nguyen. "$\mathrm{GL}^+(2,\mathbb{R})$–orbits in Prym eigenform loci." Geom. Topol. 20 (3) 1359 - 1426, 2016.


Received: 20 March 2014; Revised: 4 June 2015; Accepted: 20 July 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1368.32009
MathSciNet: MR3523060
Digital Object Identifier: 10.2140/gt.2016.20.1359

Primary: 30F30, 32G15, 37D40, 54H20‎, 57R30

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.20 • No. 3 • 2016
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