We study Alexeev and Brion's moduli scheme MΓ of affine spherical varieties with weight monoid Γ under the assumption that Γ is free. We describe the tangent space to MΓ at its “most degenerate point” in terms of the combinatorial invariants of spherical varieties and deduce that the irreducible components of MΓ, equipped with their reduced induced scheme structure, are affine spaces.
The Moduli Scheme of Affine Spherical Varieties with a Free Weight Monoid / Bravi, Paolo; Van Steirteghem, Bart. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - 2016:(2016), pp. 4544-4587. [10.1093/imrn/rnv281]
The Moduli Scheme of Affine Spherical Varieties with a Free Weight Monoid
BRAVI, Paolo;
2016
Abstract
We study Alexeev and Brion's moduli scheme MΓ of affine spherical varieties with weight monoid Γ under the assumption that Γ is free. We describe the tangent space to MΓ at its “most degenerate point” in terms of the combinatorial invariants of spherical varieties and deduce that the irreducible components of MΓ, equipped with their reduced induced scheme structure, are affine spaces.| File | Dimensione | Formato | |
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