GL^+(2,R)-orbits in Prym eigenform loci
2013
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.
Keywords:
- Correction
- Cite
- Save
- Machine Reading By IdeaReader
23
References
1
Citations
NaN
KQI