Seiberg-Witten invariants for manifolds with $b_+=1$, and the universal wall crossing formula

Abstract

In this paper we describe the Seiberg-Witten invariants, which have been introduced by Witten, for manifolds with $b_+=1$. In this case the invariants depend on a chamber structure, and there exists a universal wall crossing formula. For every Kähler surface with $p_g=0$ and $q$=0, these invariants are non-trivial for all $Spin^c(4)$-structures of non-negative index.