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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Real algebraic threefolds II. Minimal model program
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by János Kollár
J. Amer. Math. Soc. 12 (1999), 33-83


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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Bibliographic Information
  • János Kollár
  • Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
  • MR Author ID: 104280
  • Email:
  • Received by editor(s): January 26, 1998
  • © Copyright 1999 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 12 (1999), 33-83
  • MSC (1991): Primary 14E30, 14P25, 14E05; Secondary 14M20, 57N10
  • DOI:
  • MathSciNet review: 1639616