Work

Cubic fourfolds with a symplectic automorphism of prime order

Year: 2026

Type: article

Abstract: We determine the algebraic and transcendental lattices of a general cubic fourfold with a symplectic automorphism of prime order. We prove that cubic fourfolds admitting a symplectic automorphism of order at least three are rational, and we exhibit two families of rational cubic fourfolds that are not equivariantly rational with respect to their group of automorphisms. As an application, we determine the cohomological action of symplectic birational transformations of manifolds of OG10 type that are induced by prime order symplectic automorphisms of cubic fourfolds.

Source: Canadian Mathematical Bulletin

DOI: 10.4153/s0008439526101738

Authors: Simone Billi, Annalisa Grossi, Lisa Marquand

Institutions: University of Genoa, University of Bologna, New York University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: National Science Foundation, Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni