Equivariant rationality of Fano threefolds in the family \textnumero 2.12

2025/08/26 by Li, Oliver, Malbon, Joseph, Pinardin, Antoine
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.19471

Abstract

We prove that a faithful group action on the smooth complete intersection X of three divisors of bidegree (1,1) in \p³×\p³ is linearisable if and only if \rk(\pic^G(X))≠1.

Citations

• K-stability and space sextic curves of genus three
• Intermediate Jacobians and linearizability
• Equivariant geometry of singular cubic threefolds
• Equivariant geometry of odd-dimensional complete intersections of two quadrics
• Equivariant birational types and Burnside volume
• Rationality of Fano threefolds over non-closed fields

Related

• Equivariant unirationality of Fano threefolds
• A rationality criterion for real Fano threefolds
• Automorphism groups and linearizability of rational Fano conic bundle threefolds
• Equivariant geometry of singular cubic threefolds, II
• On the rationality of certain Fano threefolds