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arXiv · 1406.6041

The moduli scheme of affine spherical varieties with a free weight monoid

Paolo Bravi·Bart Van Steirteghem
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Abstract

We study Alexeev and Brion's moduli scheme $M_Γ$ of affine spherical varieties with weight monoid $Γ$ under the assumption that $Γ$ is free. We describe the tangent space to $M_Γ$ at its `most degenerate point' in terms of the combinatorial invariants of spherical varieties and deduce that the irreducible components of $M_Γ$, equipped with their reduced induced scheme structure, are affine spaces.

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Paolo Bravi, Bart Van Steirteghem. 2015-09-02. The moduli scheme of affine spherical varieties with a free weight monoid. https://doi.org/10.1093/imrn%2Frnv281

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