1998/02/10 by Janós Kollár, János Kollár, Kollár, János
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.math/9802053
LATEX2e, 40 pages
arxiv created 1998/02/10 · arxiv updated 2009/11/30
This is the third of a series of papers studying real algebraic threefolds, but the methods are mostly independent from the previous two. Let f:X→ S be a map of a smooth projective real algebraic 3-fold to a surface S whose general fibers are rational curves. Assume that the set of real points of X is an orientable 3-manifold M. The aim of the paper is to give a topological description of M. It is shown that M is either Seifert fibered or a connected sum of lens spaces. Much stronger results hold if S is rational.