This article is cited in 5 papers

Automorphisms and forms of toric quotients of homogeneous spaces

A. N. Skorobogatov<sup>ab

a</sup> Imperial College, Department of Mathematics
^b A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: We compute the automorphism group of the quotient of a generalized Grassmannian $G/P$ by the action of a maximal torus of the semisimple group $G$. We classify the twisted forms of such quotients, that is, varieties isomorphic to these quotients over an algebraic closure of the base field. It is proved that all such forms are unirational.
Bibliography: 20 titles.

Keywords: homogeneous spaces, tori, twisted forms, torsors.

UDC: 512.816.4+512.745.2

MSC: 14J50, 14L30, 14M17

Received: 29.08.2008 and 08.05.2009

DOI: 10.4213/sm7149

 English version: Sbornik: Mathematics, 2009, 200:10, 1521–1536

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