Let k be an algebraically closed field, and V be a vector space of dimension n over k. For a set w = （ d →（1）,..., d→ （m）） of sequences of positive integers, denote by Lω the ample line bundle corresponding t...Let k be an algebraically closed field, and V be a vector space of dimension n over k. For a set w = （ d →（1）,..., d→ （m）） of sequences of positive integers, denote by Lω the ample line bundle corresponding to the polarization on the product X = Пi=1 m Flag（V, →n（i）） of flag varieties of type n→（i） determined by ω. We study the SL（V）-linearization of the diagonal action of SL（V） on X with respect to Lω. We give a sufficient and necessary condition on ω such that X ss（Lω） ≠ 0 （resp., Xs（Lω） ≠ 0）. As a consequence, we characterize the SL（V）-ample cone （for the diagonal action of SL（V） on X）,which turns out to be a polyhedral convex cone.展开更多
文摘Let k be an algebraically closed field, and V be a vector space of dimension n over k. For a set w = （ d →（1）,..., d→ （m）） of sequences of positive integers, denote by Lω the ample line bundle corresponding to the polarization on the product X = Пi=1 m Flag（V, →n（i）） of flag varieties of type n→（i） determined by ω. We study the SL（V）-linearization of the diagonal action of SL（V） on X with respect to Lω. We give a sufficient and necessary condition on ω such that X ss（Lω） ≠ 0 （resp., Xs（Lω） ≠ 0）. As a consequence, we characterize the SL（V）-ample cone （for the diagonal action of SL（V） on X）,which turns out to be a polyhedral convex cone.
