Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Undulation Invariants of Plane Curves   One of the general problems in algebraic geometry is to determine
algorithmically whether or not a given geometric object, defined by explicit
polynomial equations (e.g. a curve or a surface), satisfies a given property
(e.g. has singularities or other distinctive features of interest). A classical
example of such a problem, described by A.Cayley and G.Salmon in 1852, is to
determine whether or not a given plane curve of degree r > 3 has undulation
points -- the points where the tangent line meets the curve with multiplicity
four. They proved that there exists an invariant of degree 6(r - 3)(3 r - 2)
that vanishes if and only if the curve has undulation points. In this paper we
give explicit formulae for this invariant in the case of quartics (r=4) and
quintics (r=5), expressing it as the determinant of a matrix with polynomial
entries, of sizes 21 times 21 and 36 times 36 respectively.

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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci