Donaldson = Seiberg-Witten from Mochizuki's formula and instanton counting
for the theory with a fundamental matter
Mochizuki's formula express Donaldson invariants in terms of
Seiberg-Witten invariants and certain integrals over Hilbert schemes of
points. We write the latter by the instanton counting partition
function of the theory with a fundamental matter. We then compute the
partition function in terms of elliptic integrals associated with
Seiberg-Witten curves for this theory. For the case of Mochizuki's
formula, the Seiberg-Witten curve becomes singular, and everything
become explicit. This is a joint work with Kota Yoshioka.
nakajima@math.kyoto-u.ac.jp