Gorenstein Fano Generic Torus Orbit in $G/P$

Pierre-Louis Montagard (1) , Alvaro Rittatore (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 CMAT - Centro de Matemática [Montevideo]

Given a simple algebraic group $G$ and a parabolic subgroup $P\subset G$, with maximal torus $T$, we consider the closure $X$ of a generic $T$-orbit (in the sense of Dabrowski's work) in $G/P$, and determine when $X$ is a Gorenstein-Fano variety. We deduce of this classification a list of some pairs of dual reflexive polytopes.

Domaines: Géométrie algébrique [math.AG]; Théorie des représentations [math.RT]; Combinatoire [math.CO]

Pierre-Louis Montagard, Alvaro Rittatore. Gorenstein Fano Generic Torus Orbit in $G/P$. 2021. ⟨hal-01717935v2⟩