Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing lattice surfaces with prescribed Veech groups: an algorithm   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 $\text{SL}_2\mathbb{Z}$.

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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph