Abstract
The Veech group of a translation surface is the group of Jacobians of orientation-preserving affine automorphisms of the surface. We present an algorithm which constructs all translation surfaces with a given lattice Veech group in any given stratum. In developing this algorithm, we give a new proof of a finiteness result of Smillie and Weiss, namely that there are only finitely many (unit-area) translation surfaces in any stratum with the same lattice Veech group.
Our methods can be applied to obtain obstructions of lattices being realized as Veech groups in certain strata; in particular, we show that the square torus is the only translation surface in any minimal stratum whose Veech group is all of SL2Z.
Our methods can be applied to obtain obstructions of lattices being realized as Veech groups in certain strata; in particular, we show that the square torus is the only translation surface in any minimal stratum whose Veech group is all of SL2Z.
Original language | English |
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Publisher | arXiv |
Pages | 1-28 |
DOIs | |
Publication status | Published - 29 Nov 2021 |
Keywords
- translation surfaces
- Veech group