Generalized nuclei of complex surfaces

Abstract

For each g ≥ 1, we study a family Yg(n) of complex surfaces which admit a singular fibration over ℂP1 by complex curves of genus g. By examining a handlebody description for Yg(n), we show that these complex surfaces can be smoothly decomposed as the Milnor fiber of a Brieskorn homology 3-sphere union a small submanifold, termed a "nucleus". This description generalizes known decompositions for elliptic surfaces.