SAG: The geometry of Nekrasov's gauge origami theorySeminar Algebraic Geometry (SAG)

by Martijn Kool (Utrecht)

Thursday Dec 10, 2026, 10:30 AM → 11:30 AM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

The moduli space of stable representations of the ADHM quiver plays a central role in representation theory, enumerative geometry, and gauge theory. It is non-compact, holomorphic symplectic, and isomorphic to a moduli space of framed sheaves on (CP^{^1})^{^2} by work of Barth and others. I will discuss a "4-fold" generalization of the ADHM quiver called the "origami quiver" due to Nekrasov. Although the associated moduli space of stable representations is generally singular, it is still "(-2)-shifted" holomorphic symplectic and it carries an Oh-Thomas virtual cycle leading to an origami partition function, which we calculate. Using Huybrechts-Lehn's and Spaide's work, I give a geometric description of the "derived" moduli space in terms of framed sheaves on (CP^{^1})^{^4}. Joint work with Arbesfeld-Lim.