Moduli spaces of branched covers of Veech surfaces I: d-symmetric differentials
| dc.creator | Schmoll, Martin | |
| dc.date | 2006-02-17 | |
| dc.date.accessioned | 2026-07-07T07:03:34Z | |
| dc.date.available | 2026-07-07T07:03:34Z | |
| dc.description | We give a description of asymptotic quadratic growth rates for geodesic segments on covers of Veech surfaces in terms of the modular fiber parameterizing coverings of a fixed Veech surface. To make the paper self contained we derive the necessary asymptotic formulas from the Gutkin-Judge formula. As an application of the method we define and analyze d-symmetric elliptic differentials and their modular fibers F^{sym}_d. For given genus g, g-symmetric elliptic differentials (with fixed base lattice) provide a 2-dimensional family of translation surfaces. We calculate several asymptotic constants, to establish their dependence on the translation geometry of F^{sym}_d and their sensitivity as SL(2,Z)-orbit invariants. | |
| dc.description | 40 pages, 1 figure, submitted | |
| dc.identifier | https://arxiv.org/abs/math/0602396 | |
| dc.identifier | http://arxiv.org/abs/math/0602396 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109020 | |
| dc.subject | Geometric Topology | |
| dc.subject | Dynamical Systems | |
| dc.subject | 14H15, 30F30, 30F60, 37C35, 58D27 | |
| dc.title | Moduli spaces of branched covers of Veech surfaces I: d-symmetric differentials | |
| dc.type | text |