Geodesic
Real algebraic threefolds II. Minimal model program
Kollár, János1
1 Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Journal of the American Mathematical Society, Tome 12 (1999) no. 1, pp. 33-83

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

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.
DOI : 10.1090/S0894-0347-99-00286-6

Kollár, János 1

1 Department of Mathematics, University of Utah, Salt Lake City, Utah 84112 
@article{10_1090_S0894_0347_99_00286_6,
     author = {Koll\~A{\textexclamdown}r, J\~A{\textexclamdown}nos},
     title = {Real algebraic threefolds {II.} {Minimal} model program},
     journal = {Journal of the American Mathematical Society},
     pages = {33--83},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {1999},
     doi = {10.1090/S0894-0347-99-00286-6},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-99-00286-6/}
}
TY  - JOUR
AU  - Kollár, János
TI  - Real algebraic threefolds II. Minimal model program
JO  - Journal of the American Mathematical Society
PY  - 1999
SP  - 33
EP  - 83
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-99-00286-6/
DO  - 10.1090/S0894-0347-99-00286-6
ID  - 10_1090_S0894_0347_99_00286_6
ER  - 
%0 Journal Article
%A Kollár, János
%T Real algebraic threefolds II. Minimal model program
%J Journal of the American Mathematical Society
%D 1999
%P 33-83
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-99-00286-6/
%R 10.1090/S0894-0347-99-00286-6
%F 10_1090_S0894_0347_99_00286_6
Kollár, János. Real algebraic threefolds II. Minimal model program. Journal of the American Mathematical Society, Tome 12 (1999) no. 1, pp. 33-83. doi: 10.1090/S0894-0347-99-00286-6

[1] Akbulut, S., King, H. All knots are algebraic Comment. Math. Helv. 1981 339 351

[2] Akbulut, Selman, King, Henry Topology of real algebraic sets 1992

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

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

[5] Clemens, Herbert, Kollã¡R, Jã¡Nos, Mori, Shigefumi Higher-dimensional complex geometry Astérisque 1988

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

[7] Fulton, William Introduction to toric varieties 1993

[8] Fulton, William Algebraic topology 1995

[9] Greenberg, Marvin J., Harper, John R. Algebraic topology 1981

[10] Hartshorne, Robin Algebraic geometry 1977

[11] Hempel, John 3-Manifolds 1976

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

[13] Johannson, Klaus Homotopy equivalences of 3-manifolds with boundaries 1979

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

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

[16] Kollã¡R, Jã¡Nos The structure of algebraic threefolds: an introduction to Mori’s program Bull. Amer. Math. Soc. (N.S.) 1987 211 273

[17] Kollã¡R, Jã¡Nos Minimal models of algebraic threefolds: Mori’s program Astérisque 1989

[18] Kollã¡R, Jã¡Nos, Miyaoka, Yoichi, Mori, Shigefumi Rationally connected varieties J. Algebraic Geom. 1992 429 448

[19] Kollã¡R, Jã¡Nos, Mori, Shigefumi Classification of three-dimensional flips J. Amer. Math. Soc. 1992 533 703

[20] Lyndon, Roger C., Schupp, Paul E. Combinatorial group theory 1977

[21] Markushevich, Dimitri Minimal discrepancy for a terminal cDV singularity is 1 J. Math. Sci. Univ. Tokyo 1996 445 456

[22] Matsusaka, T., Mumford, D. Two fundamental theorems on deformations of polarized varieties Amer. J. Math. 1964 668 684

[23] Moise, Edwin E. Geometric topology in dimensions 2 and 3 1977

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

[25] Mori, Shigefumi On 3-dimensional terminal singularities Nagoya Math. J. 1985 43 66

[26] Mori, Shigefumi Flip theorem and the existence of minimal models for 3-folds J. Amer. Math. Soc. 1988 117 253

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

[28] Reid, Miles Canonical 3-folds 1980 273 310

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

[30] Rolfsen, Dale Knots and links 1976

[31] Rourke, Colin Patrick, Sanderson, Brian Joseph Introduction to piecewise-linear topology 1982

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

[33] Corliss, J. J. Upper limits to the real roots of a real algebraic equation Amer. Math. Monthly 1939 334 338

[34] Silhol, Robert Real algebraic surfaces with rational or elliptic fiberings Math. Z. 1984 465 499

[35] Silhol, Robert Real algebraic surfaces 1989

[36] Viro, O. Ya. Real plane algebraic curves: constructions with controlled topology Algebra i Analiz 1989 1 73

Cité par Sources :