The Log Minimal Model Program for horospherical varieties via moment polytopes

In [Pas15], we described the Minimal Model Program in the family of Q-Gorenstein projective horospherical varieties, by studying a family of polytopes defined from the moment polytope of an ample Q-Cartier Q-divisor of the variety we begin with. Here, we summarize the results of [Pas15] and we explain how to generalize them in order to describe the Log Minimal Model Program for pairs (X,∆) where X is a projective horospherical G-variety and ∆ is a B-stable Q-divisor (where G is a connected reductive algebraic group and B a Borel subgroup of G). Mathematics Subject Classification. 14E30 14M25 52B20 14M17