Anti-symplectic involutions with lagrangian fixed loci and their quotients

We study the lagrangian embedding as a fixed point set of anti-symplectic involution $\tau$ on a symplectic 4-manifold $X$. Suppose the fixed loci of $\tau$ are the disjoint union of smooth Riemann surfaces $X^{\tau} =\dot\cup \,{\Sigma_i}$; then each component becomes a lagrangian submanifold. Furthermore, if one of the components is a Riemann surface of genus $g\ge 2$, then its quotient has vanishing Seiberg-Witten invariants. We will discuss some examples which allow an anti-symplectic involution with lagrangian fixed loci.