The blowup formula for the instanton part of Vafa-Witten invariants on projective surfaces
We prove a blow-up formula for the generating series of virtual $\chi_y $-genera for moduli
spaces of sheaves on projective surfaces, which is related to a conjectured formula for
topological $\chi_y $-genera of G\" ottsche. 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 $\mathbb
{P}^ 2$. The proof is based on the blow-up algorithm of Nakajima-Yoshioka for framed …
spaces of sheaves on projective surfaces, which is related to a conjectured formula for
topological $\chi_y $-genera of G\" ottsche. 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 $\mathbb
{P}^ 2$. The proof is based on the blow-up algorithm of Nakajima-Yoshioka for framed …
We prove a blow-up formula for the generating series of virtual -genera for moduli spaces of sheaves on projective surfaces, which is related to a conjectured formula for topological -genera of G\"ottsche. 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 . The proof is based on the blow-up algorithm of Nakajima-Yoshioka for framed sheaves on , which has recently been extend to the setting of Gieseker -stable sheaves on -polarised surfaces by Kuhn-Tanaka.
arxiv.org
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