Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized weight properties of resultants and discriminants, and
  applications to projective enumerative geometry   In a book dating back to 1862, Salmon stated a formula giving the first terms
of the Taylor expansion of the discriminant of a plane algebraic curve, and
from it derived various enumerative quantities for surfaces in $\mathbf{P}^3$.
In this text, we provide complete proofs of this formula and its enumerative
applications, and extend Salmon's considerations to hypersurfaces in a
projective space of arbitrary dimension. To this end, we extend reduced
elimination theory by introducing the concept of reduced discriminant, and
provide a thorough study of its weight properties; the latter are deeply linked
to projective enumerative geometric properties. Then, following Salmon's
approach, we compute the number of members of a pencil of hyperplanes that are
bitangent to a fixed projective hypersurface. Some other results in the same
spirit are also discussed.

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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph