On Some Families of Smooth Affine Spherical Varieties of Full Rank

Paulus K, Pezzini G, van Steirteghem B (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Acta Mathematica Sinica-English Series Springer Verlag (Germany)

Book Volume: 34

Pages Range: 563-596

Journal Issue: 3

DOI: 10.1007/s10114-018-7244-1

Abstract

Let G be a complex connected reductive group. Losev has shown that a smooth affine spherical G-variety X is uniquely determined by its weight monoid, which is the set of irreducible representations of G that occur in the coordinate ring of X. In this paper we use a combinatorial characterization of the weight monoids of smooth affine spherical varieties to classify: (a) all such varieties for G = SL(2) × ℂ × and (b) all such varieties for G simple which have a G-saturated weight monoid of full rank. We also use the characterization and Knop’s classification theorem for multiplicity free Hamiltonian manifolds to give a new proof of Woodward’s result that every reflective Delzant polytope is the moment polytope of such a manifold.

Authors with CRIS profile

Bart van Steirteghem Department Mathematik

Involved external institutions

Università degli studi "La Sapienza" IT Italy (IT)

How to cite

APA:

Paulus, K., Pezzini, G., & van Steirteghem, B. (2018). On Some Families of Smooth Affine Spherical Varieties of Full Rank. Acta Mathematica Sinica-English Series, 34(3), 563-596. https://dx.doi.org/10.1007/s10114-018-7244-1

MLA:

Paulus, Kay, Guido Pezzini, and Bart van Steirteghem. "On Some Families of Smooth Affine Spherical Varieties of Full Rank." Acta Mathematica Sinica-English Series 34.3 (2018): 563-596.

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