The Nash conjecture for threefolds

被引：6

作者：

Kollár, J ^{[1
]}

机构：

[1] Univ Utah, Salt Lake City, UT 84112 USA

来源：

ELECTRONIC RESEARCH ANNOUNCEMENTS OF THE AMERICAN MATHEMATICAL SOCIETY | 1998年 / 4卷

关键词：

D O I：

10.1090/S1079-6762-98-00049-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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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收藏

页码：63 / 73

页数：11

相关论文

共 20 条

[1] RATIONAL STRUCTURES ON 3-MANIFOLDS [J].

AKBULUT, S ;

KING, H .

PACIFIC JOURNAL OF MATHEMATICS, 1991, 150 (02) :201-214

[2] TEARS IN 3-MANIFOLDS AND THE NASH RATIONALITY CONJECTURE IN 3-SPACE [J].

BENEDETTI, R ;

MARIN, A .

COMMENTARII MATHEMATICI HELVETICI, 1992, 67 (04) :514-545

[3]

Comessatti A., 1914, ANN MATH, V3, P215, DOI 10.1007/BF02419577

[4] ELEMENTARY CONTRACTIONS OF GORENSTEIN THREEFOLDS [J].

CUTKOSKY, S .

MATHEMATISCHE ANNALEN, 1988, 280 (03) :521-525

[5]

Iskovskikh V. A., 1980, J. Soviet Math., V12, P745, DOI 10.1007/BF01084563

[6]

Kawamata, 1992, P INT C ALGEBRA, V131, P439, DOI [10.1090/conm/131.3/1175897, DOI 10.1090/CONM/131.3/1175897]

[7]

Kawamata Y, 1996, HIGHER DIMENSIONAL COMPLEX VARIETIES, P241

[8]

Kharlamov V.M., 1976, FUNCTIONAL ANAL APPL, V10, P295, DOI DOI 10.1007/BF01076029

[9] THE STRUCTURE OF ALGEBRAIC THREEFOLDS - AN INTRODUCTION TO MORI PROGRAM [J].

KOLLAR, J .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 17 (02) :211-273

[10] EFFECTIVE BASE POINT FREENESS [J].

KOLLAR, J .

MATHEMATISCHE ANNALEN, 1993, 296 (04) :595-605