Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariants of real symplectic 4-manifolds out of reducible and cuspidal
  curves   We construct invariants under deformation of real symplectic 4-manifolds.
These invariants are obtained by counting three different kinds of real
rational J-holomorphic curves which realize a given homology class and pass
through a given real configuration of (the appropriate number of) points. These
curves are cuspidal curves, reducible curves and curves with a prescribed
tangent line at some real point of the configuration. They are counted with
respect to some sign defined by the parity of their number of isolated real
double points and in the case of reducible curves, with respect to some
mutiplicity. In the case of the complex projective plane equipped with its
standard symplectic form and real structure, these invariants coincide with the
ones previously constructed in math.AG/0303145. This leads to a relation
between the count of real rational J-holomorphic curves done in math.AG/0303145
and the count of real rational reducible J-holomorphic curves presented here.

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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: nlin