Verlinde-type formulas for rational surfaces

TL;DR

This paper develops an algorithm to compute generating functions of K-theoretic Donaldson invariants on rational surfaces, providing explicit formulas and exploring their relation to Le Potier's strange duality conjecture.

Contribution

It introduces a new algorithm for calculating K-theoretic Donaldson invariants on rational surfaces, extending previous methods and linking to duality conjectures.

Findings

Explicit formulas for invariants on rational surfaces

Algorithm for generating functions of Donaldson invariants

Connections to Le Potier's strange duality conjecture

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 K-theoretic Donaldson invariants on the projective plane and more generally rational surfaces, and apply it in many cases to get explicit formulas. We relate the results to Le Potier's strange duality conjecture.