Real Algebraic Threefolds III: Conic Bundles
Abstract
Description
This is the third of a series of papers studying real algebraic threefolds, but the methods are mostly independent from the previous two. Let $f:X\to S$ 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.
LATEX2e, 40 pages
LATEX2e, 40 pages