Modular Fibers And Illumination Problems
Geometric Topology
2007-05-23 v2 Dynamical Systems
Abstract
For a Veech surface (x,\omega), we characterize subspaces of X^n, invariant under the diagonal action of the affine group of X. We prove that non-arithmetic Veech surfaces have only finitely many invariant subspaces of very particular shape (in any dimension). Among other consequences we find copies of (X,\omega) embedded in the moduli-space of translation surfaces. We study illumination problems in (pre-)lattice surfaces. For (X,\omega) prelattice we prove the at most countableness of points non-illuminable from any x in X. Applying our results on invariant subspaces we prove the finiteness of these sets when (X,\omega) is Veech.
Cite
@article{arxiv.math/0602394,
title = {Modular Fibers And Illumination Problems},
author = {Pascal Hubert and Martin Schmoll and Serge Troubetzkoy},
journal= {arXiv preprint arXiv:math/0602394},
year = {2007}
}
Comments
37 pages, 3 figures, submitted, 2/21/06 replacement contains one more figure