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In this paper we study the existence of sections of universal bundles onrational homogeneous varieties -- called nestings -- classifying themcompletely in the case in which the Lie algebra of the automorphism group ofthe variety is simple of classical type. In particular we show that, under thishypothesis, nestings do not exist unless there exists a proper algebraicsubgroup of the automorphism group acting transitively on the base variety.

Nestings of rational homogeneous varieties