Wall-crossing between stable and co-stable ADHM data

Abstract

We prove formula between Nekrasov partition functions defined from stable and co-stable ADHM data for the plane following method by Nakajima-Yoshioka based on the theory of wall-crossing formula developed by Mochizuki. This formula is similar to conjectures by Itoh-Maruyoshi-Okuda for $A_1$ singularity.

arXiv commentAdded new sections 2. Notation and outline of the paper and 7. Hilbert schemes parametrizing destabilizing objects, and deleted Appendix Integrations on Hilbert schemes. Introduced stability conditions for data in ambient spaces rather than only ADHM data. Added more explanation about obstruction theories. Corrected some typos