Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An algorithm for classifying origamis into components of Teichm\"uller
  curves   Nontrivial examples of Teichm\"uller curves have been studied systematically
with notions of combinatorics invariant under affine homeomorphisms. An origami
induces a Teichm\"uller curve for which two Galois actions are compatible: one
for the belonging curves and the embedded curve in the moduli space. In this
paper, we study general origamis admitting purely half-translation ones. Their
Teichm\"uller curves are calculated exhaustively by comparing their
`parallelogram decompositions' in some directions. We calculate the concrete
result for degree $d\leq 7$ and consider the possibility of Galois conjugacy.

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The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph