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The Nash conjecture for threefolds

Author: János Kollár
Journal: Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 63-73
MSC (1991): Primary 14P25
Published electronically: September 15, 1998
MathSciNet review: 1641168
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Abstract: 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.

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

Received by editor(s): July 17, 1998
Published electronically: September 15, 1998
Communicated by: Robert Lazarsfeld
Article copyright: © Copyright 1998 American Mathematical Society