Topological rigidity of algebraic $\P_3$-bundles over curves

Abstract

A projective algebraic surface which is homeomorphic to a ruled surface over a curve of genus $g\ge 1$ is itself a ruled surface over a curve of genus $g$. In this note, we prove the analogous result for projective algebraic manifolds of dimension 4 in case $g\ge 2$.Comment: 11 pages; To appear in the Annali di Matematica Pura ed Applicat