Spaces of elliptic differentials

Details Spaces of elliptic differentials Spaces of elliptic differentials

2006-02-17

arxiv.org/abs/math/0602392v2

Contemp. Math., 385, Amer. Math. Soc., Providence, RI, 2005

Mathematics

Geometric Topology

18 pages, 3 figures, published. Slightly improved version with updated references

Scientific paper

We study modular fibers of elliptic differentials, which are roughly spaces of torus-coverings over a fixed base torus. For genus 2 torus covers with fixed degree we show, that the modular fibers F_d(1,1) are itself connected torus covers with Veech group SL_2(Z). Using results of Eskin, Masur and Schmoll we calculate the Euler Characteristic and the parity of the spin structure of the quadratic differential (F_d(1,1)/(-id),q_d). We state and apply formulas for the asymptotic quadratic growth rates of various types of geodesic segments on a surface S "contained" in F_d(1,1). The quadratic growth rates are expressed in terms of the SL_2(Z) orbit closure of S \in F_d(1,1) and the flat geometry of F_d(1,1).

Affiliated with

Also associated with

No associations

Rating

Spaces of elliptic differentials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Spaces of elliptic differentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spaces of elliptic differentials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-471391