Lisa Jeffrey - Holomorphic bundles and the Verlinde formula

The moduli space M(n,d) of semistable holomorphic bundles of (coprime) rank n and degree d over a closed Riemann surface of genus g is a smooth Kahler manifold. We show how to use the Riemann-Roch formula and formulas for the intersection numbers in the cohomology of M(n,d) (proved in joint work with F. Kirwan) to establish the Verlinde formula, which is a formula for the dimension of the space of holomorphic sections of a line bundle over M(n,d). We also show how to extend our proof to prove a more general version of the Verlinde formula which gives the dimension of the space of holomorphic sections of line bundles over more general moduli spaces related to M(n,d).