December 20, 2022
Kjølv Egelands Hus
Europe/Oslo timezone

The Blowup Formula for the Instanton Part of Vafa-Witten Invariants on Projective Surfaces

Dec 20, 2022, 3:30 PM
E-102 (Kjølv Egelands Hus)


Kjølv Egelands Hus


Nikolas Kuhn (University of Oslo)


We prove a blow-up formula for the generating series of virtual χy-genera for moduli spaces of sheaves on projective surfaces, which is related to a conjectured formula for topological χy-genera of Göttsche. 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 ℙ2. The proof is based on the blow-up algorithm of Nakajima-Yoshioka for framed sheaves on ℙ2, which has recently been extend to the setting of Gieseker H-stable sheaves on H-polarised surfaces by Kuhn-Tanaka.

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