Classification of genus-1holomorphic Lefschetz pencils

In this paper, we classify relatively minimal genus-$1$ holomorphic Lefschetz pencils up to smooth isomorphism. We first show that such a pencil is isomorphic either the on $P^1\times P^1$ of bidegree $(2,2)$ or blow-up $P^2$ degree $3$, provided no fiber contains an embedded sphere (note one can easily with in fiber). further determine monodromy factorizations these and isomorphism class $3$ does not depend choice blown-up base points. also constructed by Korkmaz-Ozbagci (with nine points) Tanaka eight are respectively above, particular both holomorphic.