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1 results

  • Descendents on local curves: rationality

  • Part of
  • R. Pandharipande, A. Pixton
  • Journal:
    Compositio Mathematica / Volume 149 / Issue 1 / January 2013
    Published online by Cambridge University Press:
    01 November 2012, pp. 81-124
    Print publication:
    January 2013

  • We study the stable pairs theory of local curves in 3-folds with descendent insertions. The rationality of the partition function of descendent invariants is established for the full local curve geometry (equivariant with respect to the scaling 2-torus), including relative conditions and odd-degree insertions for higher-genus curves. The capped 1-leg descendent vertex (equivariant with respect to the 3-torus) is also proven to be rational. The results are obtained by combining geometric constraints with a detailed analysis of the poles of the descendent vertex.