Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Refined curve counting on complex surfaces   We define refined invariants which "count" nodal curves in sufficiently ample
linear systems on surfaces, conjecture that their generating function is
multiplicative, and conjecture explicit formulas in the case of K3 and abelian
surfaces. We also give a refinement of the Caporaso-Harris recursion, and
conjecture that it produces the same invariants in the sufficiently ample
setting. The refined recursion specializes at y = -1 to the
Itenberg-Kharlamov-Shustin recursion for Welschinger invariants. We find
similar interactions between refined invariants of individual curves and real
invariants of their versal families.

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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: nlin