Abstract
For a Veech surface (X, !), we characterize Aff + (X, !) invariant subspaces of X n and prove that non-arithmetic Veech surfaces have only finitely many invariant subspaces of very par- ticular shape (in any dimension). Among other consequences we find copies of (X, !) embedded in the moduli-space of translation surfaces. We study illumination problems in (pre-)lattice surfaces. For (X, !) prelattice we prove the at most countableness of points non-illuminable from any x ∈ X. Applying our results on invari- ant subspaces we prove the finiteness of these sets when (X, !) is Veech.
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