On the signature of a Lefschetz fibration coming from an involution

We will consider symplectic 4-manifolds as a Lefschetz fibration. The Euler characteristic of a Lefschetz fibration is easy to compute but the signature is not easy to compute. In the talk we will show that the signature of a Lefschetz fibration coming from a special involution as a product of right handed Dehn twists depends only on the number of genus located on the involution axis. We also consider a Lefschetz fibration coming from a finite order element of a mapping class group as a composition of two special involutions and we investigate the geography of such Lefschetz fibrations.