Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)



Real algebraic threefolds II.
Minimal model program

Author: János Kollár
Journal: J. Amer. Math. Soc. 12 (1999), 33-83
MSC (1991): Primary 14E30, 14P25, 14E05; Secondary 14M20, 57N10
MathSciNet review: 1639616
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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. 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 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.

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János Kollár
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112

Received by editor(s): January 26, 1998
Article copyright: © Copyright 1999 American Mathematical Society