Higher-Dimensional Losev–Manin Spaces and Their Geometry
Year: 2025
Type: article
Abstract: The classical Losev–Manin space is 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 constructed by Chen, Gibney, and Krashen is not a Mori dream space when the number of points is at least nine, regardless of the dimension.
DOI: 10.1093/imrn/rnaf347
Authors: Patricio Gallardo, Javier González-Anaya, José Luis González, Evangelos Routis
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,534
OpenAlex ID: W4416838828