SEIBERG-WITTEN INVARIANTS AND (ANTI-)SYMPLECTIC INVOLUTIONS

Let X be a closed, symplectic 4-manifold. Suppose that there is either a symplectic or an anti-symplectic involution (sigma) : X(longrightarrow)X with a 2-dimensional compact, oriented submanifold (Sigma) as a fixed point set. If (sigma) is a symplectic involution then the quotient X/(sigma) with b2+(X/(sigma))=>1 is a symplectic 4-manifold. If (sigma) is an anti-symplectic involution and (Sigma) has genus greater than 1 representing non-trivial homology class, we prove a vanishing theorem on Seiberg-Witten invariants of the quotient X/(sigma) with b2+(X/(sigma))>1. If (Sigma) is a torus with self-intersection number 0, we get a relation between the SeibergWitten invariants on X and those of X/(sigma) with b2+(X), b2+(X/(sigma))>2 which was obtained in [21] when the genus g(Sigma) >1 and (Sigma). (Sigma)=0.