Real Algebraic Threefolds II: Minimal Model Program

Details Real Algebraic Threefolds II: Minimal Model Program Real Algebraic Threefolds II: Minimal Model Program

1997-12-02

arxiv.org/abs/alg-geom/9712005v1

Mathematics

Algebraic Geometry

LATEX2e, 61 pages

Scientific paper

This is the second of a series of papers studying real algebraic threefolds using the minimal model program. The main result is the following. Let $X$ be a smooth projective real algebraic 3-fold. Assume that the set of real points is an orientable 3-manifold (this assumption can be weakened considerably). Then there is a fairly simple description on how the topology of real points changes under the minimal model program. The first application is to study the topology of real projective varieties which are birational to projective 3-space (Nash conjecture). The second application is a factorization theorem for birational maps.

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