Descendents on local curves: Stationary theory

  • Rahul Pandharipande

    ETH Zürich, Switzerland
  • A. Pixton

    Princeton University, USA
Descendents on local curves: Stationary theory cover
Download Chapter PDF

A subscription is required to access this book chapter.

Abstract

The stable pairs theory of local curves in 3-folds (equivariant with respect to the scaling 2-torus) is studied with stationary descendent insertions. Reduction rules are found to lower descendents when higher than the degree. Factorization then yields a simple proof of rationality in the stationary case and a proof of the functional equation related to inverting qq. The method yields an effective determination of stationary descendent integrals. The series Zd,(d)cap(τd(p))\mathsf{Z}^{\mathsf{cap}}_{d,(d)}( \tau_d(\mathsf{p})) plays a special role and is calculated exactly using the stable pairs vertex and an analysis of the solution of the quantum differential equation for the Hilbert scheme of points of the plane.