Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0894-0347-1991-1115788-7
MathSciNet review: 1115788
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • Gerd Faltings, Diophantine approximation on abelian varieties, Ann. of Math. (2) 133 (1991), no. 3, 549–576. MR 1109353, DOI https://doi.org/10.2307/2944319
  • V. A. Iskovskikh, Fano $3$-folds. I, Math. USSR-Izv. 11 (1977), 485-527. ---, Fano $3$-folds. II, Math. USSR-Izv. 11 (1978), 469-506. ---, Anticanonical models of three-dimensional algebraic varieties, J. Soviet Math. 13 (1980), 745-814; (1978), 469-506.
  • 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, DOI https://doi.org/10.1070/SM1990v066n01ABEH001172
  • J. Kollár, Fano varieties of large index, Vestnik Moskov Gos. Univ. (1981), 31-34. (Russian) ---, private communication. J. Kollár, Y. Miyaoka, and S. Mori, in preparation.
  • J. Kollár and T. Matsusaka, Riemann-Roch type inequalities, Amer. J. Math. 105 (1983), no. 1, 229–252. MR 692112, DOI https://doi.org/10.2307/2374387
  • T. Matsusaka, Polarized varieties with a given Hilbert polynomial, Amer. J. Math. 94 (1972), 1027–1077. MR 337960, DOI https://doi.org/10.2307/2373563
  • Shigefumi Mori, Projective manifolds with ample tangent bundles, Ann. of Math. (2) 110 (1979), no. 3, 593–606. MR 554387, DOI https://doi.org/10.2307/1971241
  • Shigefumi Mori and Shigeru Mukai, Classification of Fano $3$-folds with $B_{2}\geq 2$, Manuscripta Math. 36 (1981/82), no. 2, 147–162. MR 641971, DOI https://doi.org/10.1007/BF01170131
  • 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, DOI https://doi.org/10.1073/pnas.86.9.3000
  • 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). ---, A finiteness theorem for Fano $4$-folds, Massachusetts Institute of Technology, Cambridge, MA, preprint, 1990.
  • 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, DOI https://doi.org/10.1073/pnas.86.19.7299
  • 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, DOI https://doi.org/10.2307/1971429
  • ---, The behavior of multiplier ideal sheaves under morphisms, Massachusetts Institute of Technology, Cambridge, MA, preprint 1989. ---, An observation concering the existence of Kähler-Einstein metrics on Del Pezzo surfaces, Massachusetts Institute of Technology, Cambridge, MA, preprint, 1990.

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC: 14J45

Retrieve articles in all journals with MSC: 14J45


Additional Information

Article copyright: © Copyright 1991 American Mathematical Society