Verlinde-type formulas for rational surfaces

Abstract

$K$-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 $K$-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.