Abstract:
The canonical module for quasihomogeneous affine varieties with the property that the stabilizer of a point from the open orbit contains a maximal unipotent subgroup is described in terms of the structure of the semigroup of dominant weights defining the variety. A criterion for such a variety to be Gorenstein is also given.
Bibliography: 18 titles.
Citation:
D. I. Panyushev, “The structure of the canonical module and the Gorenstein property for some quasihomogeneous varieties”, Math. USSR-Sb., 65:1 (1990), 81–95
\Bibitem{Pan88}
\by D.~I.~Panyushev
\paper The structure of the canonical module and the Gorenstein property for some quasihomogeneous varieties
\jour Math. USSR-Sb.
\yr 1990
\vol 65
\issue 1
\pages 81--95
\mathnet{http://mi.mathnet.ru/eng/sm1769}
\crossref{https://doi.org/10.1070/SM1990v065n01ABEH001140}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=965880}
\zmath{https://zbmath.org/?q=an:0681.14029|0658.14024}
Linking options:
https://www.mathnet.ru/eng/sm1769
https://doi.org/10.1070/SM1990v065n01ABEH001140
https://www.mathnet.ru/eng/sm/v179/i1/p76
This publication is cited in the following 5 articles:
Martin Cederwall, Simon Jonsson, Jakob Palmkvist, Ingmar Saberi, “Canonical Supermultiplets and Their Koszul Duals”, Commun. Math. Phys., 405:5 (2024)
Dmitri I. Panyushev, “Casimir elements associated with Levi subalgebras of simple Lie algebras and their applications”, Advances in Mathematics, 374 (2020), 107390
Dmitri I. Panyushev, “A restriction theorem and the Poincare series forU-invariants”, Math. Ann., 301:1 (1995), 655
D. I. Panyushev, “Multiplicities of Weights of Some Representations and Convex Polytopes”, Funct. Anal. Appl., 28:4 (1994), 293–295
D. I. Panyushev, “The canonical module of a quasihomogeneous normal affine $SL_2$-variety”, Math. USSR-Sb., 73:2 (1992), 569–578
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