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Characterizing homogeneous rational projective varieties with Picard number 1 by their varieties of minimal rational tangents D. A. Timashev Moscow State University |
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Аннотация: It is well known that rational algebraic curves play a key role in the geometry of complex projective varieties, especially of Fano manifolds. In particular, on Fano manifolds of Picard number (= the 2nd Betti number) one, which are sometimes called "unipolar", one may consider rational curves of minimal degree passing through general points. Tangent directions of minimal rational curves through a general point In 90-s J.-M. Hwang and N. Mok developed a philosophy declaring that the geometry of a unipolar Fano manifold is governed by the geometry of its VMRT at a general point, as an embedded projective variety. In support of this thesis, they proposed a program of characterizing unipolar flag manifolds in the class of all unipolar Fano manifolds by their VMRT. In the following decades a number of partial results were obtained by Mok, Hwang, and their collaborators. Recently the program was successfully completed (J.-M. Hwang, Q. Li, and the speaker). The main result states that a unipolar Fano manifold Язык доклада: английский |