Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hesse curve of a Lefschtz pencil of plane curves   We prove that for a generic Lefschetz pencil of plane curves of degree $d\geq
3$ there exists a curve $H$ (called the Hesse curve of the pencil) of degree
$6(d-1)$ and genus $3(4d^2-13d+8)+1$, and such that: $(i)$ $H$ has $d^2$
singular points of multiplicity three at the base points of the pencil and
$3(d-1)^2$ ordinary nodes at the singular points of the degenerate members of
the pencil; $(ii)$ for each member of the pencil the intersection of $H$ with
this fibre consists of the inflection points of this member and the base points
of the pencil.

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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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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: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an