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.

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

References in corpus (1)

• Curves on K3 surfaces and modular forms

Cited by in corpus (7)

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