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Journal Articles Journal of Algebraic Combinatorics Year : 2023

Gorenstein Fano Generic Torus Orbit closures in $G/P$

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Abstract

Given a reductive group $G$ and a parabolic subgroup $P\subset G$, with maximal torus $T$, we consider (following Dabrowski's work) the closure $X$ of a generic $T$-orbit in $G/P$, and determine in combinatorial terms when the toric variety $X$ is $\mathbb{Q}$-Gorenstein Fano, extending in this way the classification of smooth Fano generic closures given by Voskresenski\u{\i} and Klyachko. As an application, we apply the well known correspondence between Gorenstein Fano toric varieties and reflexive polytopes in order to exhibit which reflexive polytopes correspond to generic closures --- this list includes the reflexive root polytopes.
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Dates and versions

hal-01717935 , version 1 (26-02-2018)
hal-01717935 , version 2 (15-06-2021)
hal-01717935 , version 3 (11-12-2022)

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Pierre-Louis Montagard, Alvaro Rittatore. Gorenstein Fano Generic Torus Orbit closures in $G/P$. Journal of Algebraic Combinatorics, In press. ⟨hal-01717935v3⟩
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