The blow-up formula for the instanton part of Vafa–Witten invariants on projective surfaces
Year: 2026
Type: article
Abstract: We prove a blow-up formula for the generating series of virtual χ y -genera for moduli spaces of sheaves on projective surfaces, which is related to a conjectured formula of Göttsche for topological χ y -genera.Our formula is a refinement of one by Vafa-Witten relating to S-duality.We prove the formula simultaneously in the setting of Gieseker stable sheaves on polarised surfaces and also in the setting of framed sheaves on P 2 .The proof is based on the blow-up algorithm of Nakajima-Yoshioka for framed sheaves on P 2 , which has recently been extended to the setting of Gieseker H-stable sheaves on H-polarised surfaces by Kuhn-Tanaka.
Source: Algebraic geometry
DOI: 10.14231/ag-2026-023
Authors: Nikolas Kuhn, Oliver Leigh, Yuuji Tanaka
Institution: Max Planck Institute for Mathematics
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4281726090