Descendent theory for stable pairs on toric 3-folds

TL;DR

This paper proves the rationality of descendent partition functions for stable pairs on nonsingular toric 3-folds, using geometric reduction techniques, and extends results to certain log Calabi-Yau geometries.

Contribution

It establishes the rationality of descendent and relative stable pairs partition functions on toric 3-folds and related geometries, introducing a reduction method for descendent vertices.

Findings

Rationality of descendent partition functions on toric 3-folds.

Reduction of complex vertices to simpler cases.

Extension to log Calabi-Yau geometries.

Abstract

We prove the rationality of the descendent partition function for stable pairs on nonsingular toric 3-folds. The method uses a geometric reduction of the 2- and 3-leg descendent vertices to the 1-leg case. As a consequence, we prove the rationality of the relative stable pairs partition functions for all log Calabi-Yau geometries of the form (X,K3) where X is a nonsingular toric 3-fold.