2025/01/10 by Hanlong Fang, Fang, Hanlong, Luca Schaffler +3
Engineering · Mathematics · #14D06 #14D23 #14J10 #Advanced Numerical Analysis Techniques #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2501.05822
openalex publication_date 2025/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By work of Gallardo-Kerr-Schaffler, it is known that Naruki's compactification of the moduli space of marked cubic surfaces is isomorphic to the normalization of the Kollár, Shepherd-Barron, and Alexeev compactification parametrizing pairs (S,((1)/(9)+ε)D), with D the sum of the 27 marked lines on S, and their stable degenerations. In the current paper, we show that the normalization assumption is not necessary as we prove that this KSBA compactification is smooth. Additionally, we show it is a fine moduli space. This is done by studying the automorphisms and the ℚ-Gorenstein obstructions of the stable pairs parametrized by it.