Descendents on local curves: Rationality
Abstract
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.
Cite
@article{arxiv.1011.4050,
title = {Descendents on local curves: Rationality},
author = {R. Pandharipande and A. Pixton},
journal= {arXiv preprint arXiv:1011.4050},
year = {2019}
}
Comments
Second revision. The paper includes new results constraining the poles in q of the descendent partition functions to roots of unity (Theorem 5). As a corollary, the poles in q arising in the 3-point functions of the quantum cohomology of the Hilbert schemes of points of the plane are similarly constrained. 54 pages