Abstract
The work is devoted to presenting a proof of one of the most important theorems in the birational geometry of Fano varieties.
Similar content being viewed by others
References
V. V. Shokurov, “Letters of a bi-rationalist. I. A projectivity criterion,” Cont. Math., 207, 143-152 (1997).
Yu. I. Manin, Cubic Forms [in Russian], Nauka, Moscow (1972); English transl.: North-Holland, Amsterdam (1986).
F. Campana, “On twistor spaces of the class C,” J. Diff. Geometry, 33, 541-549 (1991).
J. Kollàr, Y. Miyaoka, and S. Mori, “Rationally connected varieties,” J. Algebraic Geometry, 1, 429-448 (1992).
F. Campana, “Connexitè rationnelle des variètès de Fano,” Ann. Sci. Éc. Norm. Sup., 25, 539-545 (1992).
F. Campana, Un thèorème de finitude pour les variètès de Fano suffisamment unirèglèes, Preprint (1996).
V. V. Shokurov, “Three-dimensional log surgeries,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 56, 105-203 (1992).
V. V. Shokurov, “Anticanonical boundedness for curves,” Appendix to V. V. Nikulin “Hyperbolic reflection group methods and algebraic varieties” in: Higher Dimensional Complex Varieties, Proceedings of the International Conference held in Trento, Italy (June 15–24) (1994), pp. 321-328.
V. V. Shokurov, “3-fold log models,” J. Math. Sciences, 81, 2667-2699 (1996).
Y. Kawamata, K. Matsuda, and K. Matsuki, “Introduction to the minimal model problem,” Adv. Stud. Pure Math., 10, 283-360 (1987).
J. Kollàr et al., Flips and Abundance for Algebraic Threefolds, Astèrisque, Vol. 211 (1992).
J.-L. Colliot-Theèlène, “Arithmètique des variètès rationelles et problèmes birationnels,” Proc. Int. Conf.Math, 641-653 (1986).
J. Kollàr, “Higher direct images of dualizing sheaves,” Ann. of Math., 123, 11-42 (1986).
T. Katsura, “Theorem of Luroth and related topics,” in: Algebraic Geometric Seminar, World Scientific, Singapore (1987), pp. 41-52.
B. J. Birch and H. P. F. Swinnerton-Dyer, “The Hasse problem for rational surfaces,” J. Reine Angew. Math., 274, 164-174 (1975).
S. Mori, “Projective manifolds with ample tangent bundles,” Ann. Math., 110, 593-606 (1979).
S. S. Abhyankar “On the problem of resolution of singularities,” in: Proc. Internat. Congr. Math., Mir, Moscow (1966), pp. 469-481.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shokurov, V.V. On Rational Connectedness. Mathematical Notes 68, 652–660 (2000). https://doi.org/10.1023/A:1026631926763
Issue Date:
DOI: https://doi.org/10.1023/A:1026631926763