JournalsjemsVol. 22, No. 1pp. 151–212

Verlinde-type formulas for rational surfaces

  • Lothar Göttsche

    International Centre for Theoretical Physics, Trieste, Italy
Verlinde-type formulas for rational surfaces cover

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Abstract

KK-theoretic Donaldson invariants are holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 sheaves on surfaces. We develop an algorithm which determines the generating functions of the KK-theoretic Donaldson invariants on the projective plane and more general rational surfaces, and apply it in many cases to get explicit formulas. We relate the results to Le Potier’s strange duality conjecture.

Cite this article

Lothar Göttsche, Verlinde-type formulas for rational surfaces. J. Eur. Math. Soc. 22 (2020), no. 1, pp. 151–212

DOI 10.4171/JEMS/919