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

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Commentarii Mathematici Helvetici

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.

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Authors and Affiliations

  1. Dipartimento di Matematica, “Guido Castelnuovo”, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy, e-mail: chirivi@mat.uniroma1.it, , , , , , IT

    R. Chirivì

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  1. R. Chirivì
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Received: June 23, 2000

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Chirivì, R. Deformation and Cohen-Macaulayness of the multicone over the flag variety. Comment. Math. Helv. 76, 436–466 (2001). https://doi.org/10.1007/PL00000384

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  • DOI: https://doi.org/10.1007/PL00000384

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