The Nash conjecture for threefolds
Author:
János Kollár
Journal:
Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 63-73
MSC (1991):
Primary 14P25
DOI:
https://doi.org/10.1090/S1079-6762-98-00049-3
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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- J. Kollár, Effective Base Point Freeness, Math. Ann. 296 (1993), 595-605.
- J. Kollár, Rational Curves on Algebraic Varieties, Springer-Verlag, Ergebnisse der Math. vol. 32, 1996.
- J. Kollár, Real Algebraic Threefolds I. Terminal Singularities, Collectanea Math. (to appear).
- J. Kollár, Real Algebraic Threefolds II. Minimal Model Program, J. AMS (to appear).
- J. Kollár, Real Algebraic Threefolds III. Conic Bundles (preprint).
- J. Kollár, Real Algebraic Threefolds IV. Del Pezzo Fibrations (in preparation).
- J. Kollár, Y. Miyaoka and S. Mori, Rationally Connected Varieties, J. Alg. Geom. 1 (1992), 429-448.
- J. Kollár and S. Mori, Birational geometry of algebraic varieties, Cambridge Univ. Press, 1998 (to appear).
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- M. Manetti, Normal projective surfaces with $\rho =1, P_{-1}\geq 5$, Rend. Sem. Mat. Univ. Padova 89 (1993), 195-205.
- G. Mikhalkin, Blowup equivalence of smooth closed manifolds, Topology, 36 (1997), 287-299.
- S. Mori, Threefolds whose Canonical Bundles are not Numerically Effective, Ann. of Math. 116 (1982), 133-176.
- J. Nash, Real algebraic manifolds, Ann. Math. 56 (1952), 405-421.
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Additional Information
János Kollár
Affiliation:
University of Utah, Salt Lake City, UT 84112
MR Author ID:
104280
Email:
kollar@math.utah.edu
Received by editor(s):
July 17, 1998
Published electronically:
September 15, 1998
Communicated by:
Robert Lazarsfeld
Article copyright:
© Copyright 1998
American Mathematical Society