An approach of the Minimal Model Program for horospherical varieties via moment polytopes

Boris Pasquier (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We describe the Minimal Model Program in the family of $\mathbb{Q}$-Gorenstein projective horospherical varieties, by studying a family of polytopes defined from the moment polytope of a Cartier divisor of the variety we begin with. In particular, we generalize the results on MMP in toric varieties due to M.~Reid, and we complete the results on MMP in spherical varieties due to M.~Brion in the case of horospherical varieties.

Mots clés: Moment polytopes; Minimal Model Program; Horospherical varieties; toric varieties

Domaines: Géométrie algébrique [math.AG]

Boris Pasquier. An approach of the Minimal Model Program for horospherical varieties via moment polytopes. Journal für die reine und angewandte Mathematik, 2015, 708, pp.173-212. ⟨10.1515/crelle-2013-0103⟩. ⟨hal-00757355⟩