Descendents on local curves: rationality

R. Pandharipande, A. Pixton
2012 Compositio Mathematica  
AbstractWe 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
more » ... combining geometric constraints with a detailed analysis of the poles of the descendent vertex.
doi:10.1112/s0010437x12000498 fatcat:fb2kwc7yivgznein4fdujwt4ga