Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadratic differentials and circle patterns on complex projective tori   Given a triangulation of a closed surface, we consider a cross ratio system
that assigns a complex number to every edge satisfying certain polynomial
equations per vertex. Every cross ratio system induces a complex projective
structure together with a circle pattern on the closed surface. In particular,
there is an associated conformal structure. We show that for any triangulated
torus, the projection from the space of cross ratio systems with prescribed
Delaunay angles to the Teichm\"{u}ller space is a covering map with at most one
branch point. Our approach is based on a notion of discrete holomorphic
quadratic differentials.

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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: q-bio