Generalized nuclei of complex surfaces

Terry Fuller

Vol. 187 (1999), No. 2, 281–295

DOI: 10.2140/pjm.1999.187.281

Abstract

For each g ≥ 1, we study a family Y _g(n) of complex surfaces which admit a singular fibration over ℂP¹ by complex curves of genus g. By examining a handlebody description for Y _g(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.

Milestones

Received: 10 June 1997

Revised: 9 November 1997

Published: 1 February 1999