Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Irreducibility of Equisingular Families of Curves   In 1985 Joe Harris proved the long standing claim of Severi that equisingular
families of nodal plane curves are irreducible whenever they are non-empty. For
families with more complicated singularities this is no longer true. Given a
divisor D on a smooth projective surface S it thus makes sense to look for
conditions which ensure that the family V_D(S_1,...,S_r) of irreducible curves
in the linear system |D| with precisely r singular points of types S_1,...,S_r
is irreducible. Considering different surfaces including general surfaces in
P^3 and products of curves, we produce a sufficient condition of the type
deg(X(S_1))^2 +...+ deg(X(S_r))^2 < a*(D-K_S)^2, where a is some constant and
X(S_i) some zero-dimensional scheme associated to the singularity type. Our
results carry the same asymptotics as the best known results in this direction
in the plane case, even though the coefficient is worse. For most of the
considered surfaces these are the only known results in that direction.

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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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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: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys