Configurations of points on a line up to scaling or translation

2021/02/22 by Zahariuc, Adrian
#14H10 #14L30 #14M27 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.11357

Abstract

We prove that the Losev--Manin compactification of the space of configurations of n points on \mathbb P¹ \backslash \0,∞\ modulo scaling degenerates (isotrivially) to a compactification of the space of configurations of n points on \mathbb A¹ modulo translation. The latter resembles the compactification constructed by Ziltener and Mau--Woodward, but allows the marked points to coincide, making it a \mathbb G_a^n-1-variety, which mirrors the fact that the Losev--Manin space is toric. The degeneration is compatible with the actions of \mathbb G_m^n-1 and \mathbb G_a^n-1 in the sense that these actions fit together globally in the total space of the degeneration.

Related

• Point Configurations and Translations
• Toric structure of the moduli space of points in projective space
• Higher-dimensional Losev-Manin spaces and their geometry
• Weighted compactifications of configuration spaces and relative stable degenerations
• Wonderful compactifications of the moduli space of points in affine and\n projective space