Blowup formulas for Segre and Verlinde numbers of surfaces and higher rank Donaldson invariants

2021/09/27 by Göttsche, Lothar
#14D20 (primary) 14N10 (secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.13144

Abstract

We formulate conjectural blowup formulas for Segre and Verlinde numbers on moduli spaces of sheaves on projective surfaces S with p_g(S)>0 and b₁(S)=0. As applications we give a give a conjectural formula for the Donaldson invariants of S in arbitrary rank, as well as for the K-theoretic Donaldson invariants, and some Donaldson invariants with fundamental matters.

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• Verlinde-type formulas for rational surfaces
• Probing Moduli Spaces of Sheaves with Donaldson and Seiberg Witten Invariants
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• Donaldson and Seiberg-Witten invariants of algebraic surfaces
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