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- W4385890395 abstract "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." @default.
- W4385890395 created "2023-08-17" @default.
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- W4385890395 date "2023-08-15" @default.
- W4385890395 modified "2023-09-27" @default.
- W4385890395 title "Higher-dimensional Losev-Manin spaces and their geometry" @default.
- W4385890395 doi "https://doi.org/10.48550/arxiv.2308.07911" @default.
- W4385890395 hasPublicationYear "2023" @default.
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