Descendents on local curves: Rationality

Details Descendents on local curves: Rationality Descendents on local curves: Rationality

2010-11-17

arxiv.org/abs/1011.4050v3

Mathematics

Algebraic Geometry

Revised version. The paper includes new results constraining the poles in q of the descendent partition functions to roots of

Scientific paper

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.

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