# Descendents for stable pairs on 3-folds

## TL;DR

This paper surveys the construction and properties of descendent invariants in stable pairs theory on 3-folds, highlighting key results, conjectures, and open questions in the field.

## Contribution

It provides a comprehensive overview of descendent invariants in stable pairs theory, including their properties, conjectural frameworks, and connections to other theories.

## Key findings

- Rationality of generating series established
- Functional equations for invariants discussed
- Connections to Gromov-Witten theory and Virasoro constraints explored

## Abstract

We survey here the construction and the basic properties of descendent invariants in the theory of stable pairs on nonsingular projective 3-folds. The main topics covered are the rationality of the generating series, the functional equation, the Gromov-Witten/Pairs correspondence for descendents, the Virasoro constraints, and the connection to the virtual fundamental class of the stable pairs moduli space in algebraic cobordism. In all of these directions, the proven results constitute only a small part of the conjectural framework. A central goal of the article is to introduce the open questions as simply and directly as possible.