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The boundedness of degree of Fano varieties with Picard number one
Author:
Alan Michael Nadel
Journal:
J. Amer. Math. Soc. 4 (1991), 681-692
MSC:
Primary 14J45
MathSciNet review:
1115788
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References |
Similar Articles |
Additional Information
- [F]
Gerd
Faltings, Diophantine approximation on abelian varieties, Ann.
of Math. (2) 133 (1991), no. 3, 549–576. MR 1109353
(93d:11066), http://dx.doi.org/10.2307/2944319
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V. A. Iskovskikh, Fano
-folds. I, Math. USSR-Izv. 11 (1977), 485-527.
- [I2]
-, Fano
-folds. II, Math. USSR-Izv. 11 (1978), 469-506.
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-, Anticanonical models of three-dimensional algebraic varieties, J. Soviet Math. 13 (1980), 745-814; (1978), 469-506.
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V.
A. Iskovskikh, Double projection from a line onto Fano 3-folds of
the first kind, Mat. Sb. 180 (1989), no. 2,
260–278 (Russian); English transl., Math. USSR-Sb.
66 (1990), no. 1, 265–284. MR 993458
(90j:14048)
- [K1]
J. Kollár, Fano varieties of large index, Vestnik Moskov Gos. Univ. (1981), 31-34. (Russian)
- [K2]
-, private communication.
- [KMiMo]
J. Kollár, Y. Miyaoka, and S. Mori, in preparation.
- [KMa]
J.
Kollár and T.
Matsusaka, Riemann-Roch type inequalities, Amer. J. Math.
105 (1983), no. 1, 229–252. MR 692112
(85c:14007), http://dx.doi.org/10.2307/2374387
- [Ma]
T.
Matsusaka, Polarized varieties with a given Hilbert
polynomial, Amer. J. Math. 94 (1972),
1027–1077. MR 0337960
(49 #2729)
- [Mo]
Shigefumi
Mori, Projective manifolds with ample tangent bundles, Ann. of
Math. (2) 110 (1979), no. 3, 593–606. MR 554387
(81j:14010), http://dx.doi.org/10.2307/1971241
- [MoMu]
Shigefumi
Mori and Shigeru
Mukai, Classification of Fano 3-folds with
𝐵₂≥2, Manuscripta Math. 36
(1981/82), no. 2, 147–162. MR 641971
(83f:14032), http://dx.doi.org/10.1007/BF01170131
- [Mu]
Shigeru
Mukai, Biregular classification of Fano 3-folds and Fano manifolds
of coindex 3, Proc. Nat. Acad. Sci. U.S.A. 86 (1989),
no. 9, 3000–3002. MR 995400
(90g:14024), http://dx.doi.org/10.1073/pnas.86.9.3000
- [N1]
A. M. Nadel, lecture at the JAMI Conference (The Johns Hopkins Unversity, November 7, 1990); lecture at the joint Los Angeles-Salt Lake City Conference on Algebraic Geometry (Salt Lake City, November 17, 1990); lecture at the Osaka International Conference on Complex Geometry (Osaka, December 12, 1990).
- [N2]
-, A finiteness theorem for Fano
-folds, Massachusetts Institute of Technology, Cambridge, MA, preprint, 1990.
- [N3]
Alan
Michael Nadel, Multiplier ideal sheaves and existence of
Kähler-Einstein metrics of positive scalar curvature, Proc. Nat.
Acad. Sci. U.S.A. 86 (1989), no. 19, 7299–7300.
MR
1015491 (90k:32061), http://dx.doi.org/10.1073/pnas.86.19.7299
- [N4]
Alan
Michael Nadel, Multiplier ideal sheaves and Kähler-Einstein
metrics of positive scalar curvature, Ann. of Math. (2)
132 (1990), no. 3, 549–596. MR 1078269
(92d:32038), http://dx.doi.org/10.2307/1971429
- [N5]
-, The behavior of multiplier ideal sheaves under morphisms, Massachusetts Institute of Technology, Cambridge, MA, preprint 1989.
- [N6]
-, An observation concering the existence of Kähler-Einstein metrics on Del Pezzo surfaces, Massachusetts Institute of Technology, Cambridge, MA, preprint, 1990.
- [F]
- G. Faltings, Diophantine approximation on abelian varieties, preprint. MR 1109353 (93d:11066)
- [I1]
- V. A. Iskovskikh, Fano
-folds. I, Math. USSR-Izv. 11 (1977), 485-527.
- [I2]
- -, Fano
-folds. II, Math. USSR-Izv. 11 (1978), 469-506.
- [I3]
- -, Anticanonical models of three-dimensional algebraic varieties, J. Soviet Math. 13 (1980), 745-814; (1978), 469-506.
- [I4]
- -, Double projection from a line on Fano threefolds of the first species, Math. USSR-Sb. 66 (1) (1990), 265-284. MR 993458 (90j:14048)
- [K1]
- J. Kollár, Fano varieties of large index, Vestnik Moskov Gos. Univ. (1981), 31-34. (Russian)
- [K2]
- -, private communication.
- [KMiMo]
- J. Kollár, Y. Miyaoka, and S. Mori, in preparation.
- [KMa]
- J. Kollár and T. Matsusaka, Riemann-Roch type inequalities, Amer. J. Math. 105 (1983), 229-252. MR 692112 (85c:14007)
- [Ma]
- T. Matsusaka, Polarised varieties with given Hilbert polynomial, Amer. J. Math. 94 (1972), 1027-1077. MR 0337960 (49:2729)
- [Mo]
- S. Mori, Projective manifolds with ample tangent bundles, Ann. of Math. 110 (1979), 593-606. MR 554387 (81j:14010)
- [MoMu]
- S. Mori and S. Mukai, Classification of Fano threefolds with
, Manuscripta Math. 39 (1981), 147-162. MR 641971 (83f:14032)
- [Mu]
- S. Mukai, Biregular classification of Fano
-folds and Fano manifolds of coindex 3, Proc. Nat. Acad. Sci. U.S.A. 86 (1989), 3000-3002. MR 995400 (90g:14024)
- [N1]
- A. M. Nadel, lecture at the JAMI Conference (The Johns Hopkins Unversity, November 7, 1990); lecture at the joint Los Angeles-Salt Lake City Conference on Algebraic Geometry (Salt Lake City, November 17, 1990); lecture at the Osaka International Conference on Complex Geometry (Osaka, December 12, 1990).
- [N2]
- -, A finiteness theorem for Fano
-folds, Massachusetts Institute of Technology, Cambridge, MA, preprint, 1990.
- [N3]
- -, Multiplier ideal sheaves and existence of Kähler-Einstein metrics of positive scalar curvature, Proc. Nat. Acad. Sci. U.S.A. 86 (1989), 7299-7300. MR 1015491 (90k:32061)
- [N4]
- -, Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature, Ann. of Math. (2) 132 (1990), 549-596. MR 1078269 (92d:32038)
- [N5]
- -, The behavior of multiplier ideal sheaves under morphisms, Massachusetts Institute of Technology, Cambridge, MA, preprint 1989.
- [N6]
- -, An observation concering the existence of Kähler-Einstein metrics on Del Pezzo surfaces, Massachusetts Institute of Technology, Cambridge, MA, preprint, 1990.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0894-0347-1991-1115788-7
PII:
S 0894-0347(1991)1115788-7
Article copyright:
© Copyright 1991 American Mathematical Society
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