Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tritangents and Their Space Sextics   Two classical results in algebraic geometry are that the branch curve of a
del Pezzo surface of degree 1 can be embedded as a space sextic curve and that
every space sextic curve has exactly 120 tritangents corresponding to its odd
theta characteristics. In this paper we revisit both results from the
computational perspective. Specifically, we give an algorithm to construct
space sextic curves that arise from blowing up projective plane at eight points
and provide algorithms to compute the 120 tritangents and their Steiner system
of any space sextic. Furthermore, we develop efficient inverses to the
aforementioned methods. We present an algorithm to either reconstruct the
original eight points in the projective plane from a space sextic or certify
that this is not possible. Moreover, we extend a construction of Lehavi which
recovers a space sextic from its tritangents and Steiner system. All algorithms
in this paper have been implemented in magma.

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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex