2023/08/15 by Gallardo, Patricio, González-Anaya, Javier, González, José Luis +1 · 2 citations
#14C05 #14D06 #14D20 (Primary) 14M25 #14E30 #14L30 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2308.07911
The classical Losev-Manin space can be interpreted as a toric compactification of the moduli space of n points in the affine line modulo translation and scaling. Motivated by this, we study its higher-dimensional toric counterparts, which compactify the moduli space of n distinct labeled points in affine space modulo translation and scaling. We show that these moduli spaces are a fibration over a product of projective spaces -- with fibers isomorphic to the Losev-Manin space -- and that they are isomorphic to the normalization of a Chow quotient. Moreover, we present a criterion to decide whether the blow-up of a toric variety along the closure of a subtorus is a Mori dream space. As an application, we demonstrate that a related generalization of the moduli space of pointed rational curves proposed by Chen, Gibney, and Krashen is not a Mori dream space when the number of points is at least nine, regardless of the dimension.