Real algebraic threefolds II. Minimal model program

Abstract

This is the second of a series of papers studying real algebraic threefolds using the minimal model program. The main result is the following. LetXXbe 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 of how the topology of real points changes under the minimal model program. This leads to the solution of the Nash conjecture concerning the topology of real projective varieties which are birational to projective 3-space. Another application is a factorization theorem for birational maps.