Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The moduli space of n points on the line is cut out by simple quadrics
  when n is not six   A central question in invariant theory is that of determining the relations
among invariants. Geometric invariant theory quotients come with a natural
ample line bundle, and hence often a natural projective embedding. This
question translates to determining the equations of the moduli space under this
embedding. This note deals with one of the most classical quotients, the space
of ordered points on the projective line. We show that under any linearization,
this quotient is cut out (scheme-theoretically) by a particularly simple set of
quadric relations, with the single exception of the Segre cubic threefold (the
space of six points with equal weight). Unlike many facts in geometric
invariant theory, these results (at least for the stable locus) are
field-independent, and indeed work over the integers.

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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: patt-sol