Some blowup formulas for SU(2) Donaldson polynomials (Q1340159)

If both summands of a connected sum decomposition of a 4-manifold have \(b^2_+ > 0\) then Donaldson's vanishing theorem says that all his polynomial invariants vanish. This leaves open the question how these invariants behave under addition of negative definite 4-manifolds as \(- CP^2\). (This operation is the same process as blowing up an algebraic surface.) It is conjectured that the Donaldson invariants of \(X \# -CP^2\) can be expressed in terms of the Donaldson invariants of \(X\) (when evaluated at the right cohomology classes) in a ``linear'' way. Such an expression was known up to degree 6 and it is proved in this paper up to degree 10 using Taubes's local description of the moduli space for a connected sum.