Modular Fibers And Illumination Problems

Pascal Hubert; Martin Schmoll; Serge Troubetzkoy

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Modular Fibers And Illumination Problems

Pascal Hubert·Martin Schmoll·Serge Troubetzkoy

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Abstract

For a Veech surface (x,ω), 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,ω) embedded in the moduli-space of translation surfaces. We study illumination problems in (pre-)lattice surfaces. For (X,ω) 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,ω) is Veech.

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BibTeX RIS

Pascal Hubert, Martin Schmoll, Serge Troubetzkoy. 2006-02-21. Modular Fibers And Illumination Problems. https://arxiv.org/abs/math/0602394

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