JournalscmhVol. 76 , No. 3DOI 10.1007/pl00000384

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

  • R. Chirivì

    Università di Roma La Sapienza, Italy
Deformation and Cohen-Macaulayness of the multicone over the flag variety cover

Abstract

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.