Year: 2025
Type: article
Abstract: 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 (KSBA) compactification parametrizing pairs ( S , ( 1 9 + ε ) D ) \left (S,\left (\frac {1}{9}+\varepsilon \right )D\right ) , with D D the sum of the 27 27 marked lines on S 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 \mathbb {Q} -Gorenstein obstructions of the stable pairs parametrized by it.
DOI: 10.1090/proc/17404
Authors: Hanlong Fang, Luca Schaffler, Xian Wu
Institutions: Peking University, Roma Tre University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1077915635, G192111045, G198575040, G204642360, G2156254918, G273547562, G280902537, G294099760, G4228921268, G4274909796, G4427357860, G4462815736, G4576800378, G552507481, G5915383509, G6486451614, G6542758844, G6643301752, G7193367773, G7210149476, G7643897218, G7769752610, G8140516322, G8764297080
OpenAlex ID: W4415620089