Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determining the automorphism group of a hyperelliptic curve   In this note we discuss techniques for determining the automorphism group of
a genus $g$ hyperelliptic curve $\X_g$ defined over an algebraically closed
field $k$ of characteristic zero. The first technique uses the classical $GL_2
(k)$-invariants of binary forms. This is a practical method for curves of small
genus, but has limitations as the genus increases, due to the fact that such
invariants are not known for large genus.
  The second approach, which uses dihedral invariants of hyperelliptic curves,
is a very convenient method and works well in all genera. First we define the
normal decomposition of a hyperelliptic curve with extra automorphisms. Then
dihedral invariants are defined in terms of the coefficients of this normal
decomposition. We define such invariants independently of the automorphism
group $\Aut (\X_g)$. However, to compute such invariants the curve is required
to be in its normal form. This requires solving a nonlinear system of
equations.
  We find conditions in terms of classical invariants of binary forms for a
curve to have reduced automorphism group $A_4$, $S_4$, $A_5$. As far as we are
aware, such results have not appeared before in the literature.

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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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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: physics
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The categories of this paper are: hep-th