  We investigate blowup formulae in Donaldson-Witten theory with gauge group
SU(N), using the theory of hyperelliptic Kleinian functions. We find that the
blowup function is a hyperelliptic sigma-function and we describe an explicit
procedure to expand it in terms of the Casimirs of the gauge group up to
arbitrary order. As a corollary, we obtain a new expression for the contact
terms and we show that the correlation functions involving the exceptional
divisor are governed by the KdV hierarchy. We also show that, for manifolds of
simple type, the blowup function becomes a tau-function for a multisoliton
solution.

High Energy Physics - Theory;Algebraic Geometry