Homotopy type of complements of fiber-type curves

Abstract

In this note we study the homotopy type of the complement of a plane projective curve of fiber-type. Roughly speaking, a curve of fiber-type is a finite union of fibers of a pencil. Under some restrictions, a full description of their homotopy type is given. In the context of fiber-type curves, we also partially answer in the positive a question originally posed by Libgober on the homotopy type of complements of plane curves, namely, whether or not the homotopy type of a curve complement is determined by the fundamental group and its Euler characteristic.