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.
Cite this article
R. Chirivì, Deformation and Cohen-Macaulayness of the multicone over the flag variety. Comment. Math. Helv. 76 (2001), no. 3, pp. 436–466DOI 10.1007/PL00000384