Geodesic
The Nash conjecture for threefolds
Kollár, János1
1 University of Utah, Salt Lake City, UT 84112
Electronic research announcements of the American Mathematical Society, Tome 04 (1998), pp. 63-73.

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S1079-6762-98-00049-3

Kollár, János 1

1 University of Utah, Salt Lake City, UT 84112 
@article{ERAAMS_1998_04_a9,
     author = {Koll\'ar, J\'anos},
     title = {The {Nash} conjecture for threefolds},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {63--73},
     publisher = {mathdoc},
     volume = {04},
     year = {1998},
     doi = {10.1090/S1079-6762-98-00049-3},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-98-00049-3/}
}
TY  - JOUR
AU  - Kollár, János
TI  - The Nash conjecture for threefolds
JO  - Electronic research announcements of the American Mathematical Society
PY  - 1998
SP  - 63
EP  - 73
VL  - 04
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-98-00049-3/
DO  - 10.1090/S1079-6762-98-00049-3
ID  - ERAAMS_1998_04_a9
ER  - 
%0 Journal Article
%A Kollár, János
%T The Nash conjecture for threefolds
%J Electronic research announcements of the American Mathematical Society
%D 1998
%P 63-73
%V 04
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-98-00049-3/
%R 10.1090/S1079-6762-98-00049-3
%F ERAAMS_1998_04_a9
Kollár, János. The Nash conjecture for threefolds. Electronic research announcements of the American Mathematical Society, Tome 04 (1998), pp. 63-73. doi : 10.1090/S1079-6762-98-00049-3. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-98-00049-3/

[1] Akbulut, Selman, King, Henry Rational structures on 3-manifolds Pacific J. Math. 1991 201 214

[2] Arnol′D, V. I., Guseĭn-Zade, S. M., Varchenko, A. N. Singularities of differentiable maps. Vol. I 1985

[3] Benedetti, Riccardo, Marin, Alexis Déchirures de variétés de dimension trois et la conjecture de Nash de rationalité en dimension trois Comment. Math. Helv. 1992 514 545

[4] Bochnak, J., Coste, M., Roy, M.-F. Géométrie algébrique réelle 1987

[5] Clemens, Herbert, Kollár, János, Mori, Shigefumi Higher-dimensional complex geometry Astérisque 1988

[6] Cutkosky, Steven Elementary contractions of Gorenstein threefolds Math. Ann. 1988 521 525

[7] Hartshorne, Robin Algebraic geometry 1977

[8] Hempel, John 3-Manifolds 1976

[9] Tjurin, A. N. The intermediate Jacobian of three-dimensional varieties 1979

[10] Kawamata, Yujiro Boundedness of 𝐐-Fano threefolds 1992 439 445

[11] Kawamata, Yujiro Divisorial contractions to 3-dimensional terminal quotient singularities 1996 241 246

[12] Harlamov, V. M. Topological types of nonsingular surfaces of degree 4 in 𝑅𝑃³ Funkcional. Anal. i Priložen. 1976 55 68

[13] Kollár, János The structure of algebraic threefolds: an introduction to Mori’s program Bull. Amer. Math. Soc. (N.S.) 1987 211 273

[14] Kollár, János Effective base point freeness Math. Ann. 1993 595 605

[15] Kollár, János Rational curves on algebraic varieties 1996

[16] Kollár, János, Miyaoka, Yoichi, Mori, Shigefumi Rationally connected varieties J. Algebraic Geom. 1992 429 448

[17] Manetti, Marco Normal degenerations of the complex projective plane J. Reine Angew. Math. 1991 89 118

[18] Manetti, Marco Normal projective surfaces with 𝜌 Rend. Sem. Mat. Univ. Padova 1993 195 205

[19] Mikhalkin, G. Blowup equivalence of smooth closed manifolds Topology 1997 287 299

[20] Mori, Shigefumi Threefolds whose canonical bundles are not numerically effective Ann. of Math. (2) 1982 133 176

[21] Hebroni, P. Sur les inverses des éléments dérivables dans un anneau abstrait C. R. Acad. Sci. Paris 1939 285 287

[22] Reid, Miles Young person’s guide to canonical singularities 1987 345 414

[23] Reid, Miles Nonnormal del Pezzo surfaces Publ. Res. Inst. Math. Sci. 1994 695 727

[24] Rolfsen, Dale Knots and links 1976

[25] Scott, Peter The geometries of 3-manifolds Bull. London Math. Soc. 1983 401 487

[26] Shafarevich, I. R. Osnovy algebraicheskoĭ geometrii 1972

[27] Tognoli, A. Su una congettura di Nash Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 1973 167 185

Cité par Sources :