Vyacheslav Shokurov
| Vyacheslav Shokurov | |
|---|---|
 |
|
| Born |
18 May 1950 Moscow, USSR |
| Fields | Mathematics, algebraic geometry |
| Institutions |
Johns Hopkins University Steklov Institute of Mathematics |
| Alma mater | Moscow State University |
| Doctoral advisor | Yuri Manin |
Vyacheslav Vladimirovich Shokurov (Russian: Вячеслав Владимирович Шокуров; born 18 May 1950) is a Russian mathematician best known for his research in algebraic geometry. The proof of the Noether–Enriques–Petri theorem, the cone theorem, the existence of a line on smooth Fano varieties and, finally, the existence of log flips—these are several of Shokurov's major contributions to the subject.
In 1968 Shokurov became a student of the Faculty of Mechanics and Mathematics of Moscow State University. Already as an undergraduate, Shokurov showed himself to be a mathematician of outstanding talent. In 1970, he proved the scheme analog of the Noether–Enriques–Petri theorem, which later allowed him to solve a Schottky-type problem for the polarized Prym varieties, and to prove the existence of a line on smooth Fano varieties.
Upon his graduation Shokurov entered the Ph.D. program in Moscow State University under the supervision of Yuri Manin. At this time Shokurov studied the geometry of Kuga varieties. The results obtained in this area became the body of his thesis and he was awarded his Ph.D. ("candidate degree") in 1976.
V. V. Shokurov is most famous for his work on birational geometry of algebraic varieties. After obtaining Ph.D. he worked in Yaroslavl State Pedagogical University together with Zalman Skopec. It was Skopec and another colleague, Vasily Iskovskikh, who influenced considerably the development of mathematical interests of Shokurov at that time. Iskovskikh, who was working on the classification of three-dimensional smooth Fano varieties of principal series, posed two classical problems to Shokurov: the existence of a line on smooth Fano varieties and the smoothness of a general element in the anticanonical linear system of any such variety. Shokurov solved both of these problems for three-dimensional Fano varieties and the methods which he introduced for this purpose were later developed in the works of other mathematicians, who generalized Shokurov's ideas to the case of higher-dimensional Fano varieties, and even to the Fano varieties with (admissible) singularities.
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