Commentarii Mathematici Helvetici


Full-Text PDF (570 KB) | Metadata | Table of Contents | CMH summary
Volume 76, Issue 3, 2001, pp. 436–466
DOI: 10.1007/PL00000384

Published online: 2001-09-30

Deformation and Cohen-Macaulayness of the multicone over the flag variety

R. Chirivì[1]

(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