The one-legged K-theoretic vertex of fourfolds from 3d gauge theory

TL;DR

This paper derives formulas for the K-theoretic Pandharipande-Thomas vertex of fourfolds with one non-trivial leg, using computations from a 3D supersymmetric gauge theory to connect geometric invariants with gauge theory data.

Contribution

It introduces explicit formulas for the K-theoretic vertex of fourfolds with one leg, derived from gauge theory computations, advancing the understanding of enumerative invariants in algebraic geometry.

Findings

Formulas for the K-theoretic PT vertex of fourfolds with one leg.

Identification of gauge theory boundary conditions corresponding to the vertex.

Connection between supersymmetric gauge theory and enumerative geometry.

Abstract

We present formulas for the K-theoretic Pandharipande-Thomas vertex of fourfolds, for the case of one non-trivial leg. They are obtained from computations in a three-dimensional supersymmetric gauge theory, where we identify the field content and boundary conditions that correspond to the vertex with tautological insertions.