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Classification of $G$-varieties of complexity 1

D. A. Timashev

M. V. Lomonosov Moscow State University

Abstract: We consider the problem of finding a combinatorial description of the algebraic varieties in a given birational class that admit an action of a reductive group $G$. This is a direct generalization of the theory of toric varieties. A general approach to this problem is described, and the solution is given for varieties in which the orbits in general position of a Borel subgroup $G$ have codimension 1 (varieties of complexity 1).

MSC: 14L30, 14M17, 52B99

Received: 17.05.1996

DOI: 10.4213/im119

 English version: Izvestiya: Mathematics, 1997, 61:2, 363–397

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