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Nash conjectured in 1952 that every compact differentiable manifold can be realized as the set of real points of a real algebraic variety which is birational to projective space. This paper announces the negative solution of this conjecture in dimension 3. The proof shows that in fact very few 3-manifolds can be realized this way.

Copyright 1998 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 04 (1998), pp. 63-73
• Publisher Identifier: S 1079-6762(98)00049-3
• 1991 Mathematics Subject Classification. Primary 14P25
• Key words and phrases.
• Received by the editors July 17, 1998
• Posted on September 15, 1998
• Communicated by Robert Lazarsfeld
• Comments (When Available)

J\'anos Koll\'ar

University of Utah, Salt Lake City, UT 84112

E-mail address: kollar@math.utah.edu