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Journal Articles International Mathematics Research Notices Year : 2008

Modular Fibers And Illumination Problems


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.

Dates and versions

hal-00362166 , version 1 (17-02-2009)



Pascal Hubert, Martin Schmoll, Serge Troubetzkoy. Modular Fibers And Illumination Problems. International Mathematics Research Notices, 2008, 8, Art. ID rnn011, 42 pp. ⟨10.1093/imrn/rnn011⟩. ⟨hal-00362166⟩
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