Commentarii Mathematici Helvetici
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Published online: 2001-09-30
Deformation and Cohen-Macaulayness of the multicone over the flag varietyR. Chirivì (1) Università di Roma La Sapienza, Italy
A general theory of LS algebras over a multiposet is developed. As a main result, the existence of a flat deformation to discrete algebras is obtained. This is applied to the multicone over partial flag varieties for Kac-Moody groups proving a deformation theorem to a union of toric varieties. In order to achieve the Cohen-Macaulayness of the multicone we show that Bruhat posets (defined as glueing of minimal representatives modulo parabolic subgroups of a Weyl group) are lexicographically shellable.
Keywords: Multicone, flag variety, standard monomial theory, Bruhat order, shellability
Chirivì R.: Deformation and Cohen-Macaulayness of the multicone over the flag variety. Comment. Math. Helv. 76 (2001), 436-466. doi: 10.1007/PL00000384