This article is cited in 34 papers

Toroidal Fano varieties and root systems

V. E. Voskresenskii, A. A. Klyachko


Abstract: In this paper it is shown that over an algebraically closed field there exist only finitely many mutually nonisomorphic toroidal Fano varieties. We give a complete description of toroidal Fano varieties with a centrally symmetric fan. We prove the rationality of a special class of toroidal Fano varieties and consider applications to problems of rationality of algebraic groups.
Bibliography: 17 titles.

UDC: 512.7

MSC: Primary 14J40, 14L30; Secondary 14M20, 17B20

Received: 01.10.1982
Revised: 08.02.1983

 English version: Mathematics of the USSR-Izvestiya, 1985, 24:2, 221–244

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