Automorphism groups and linearizability of rational Fano conic bundle threefolds

2025/06/18 by Abe, Shuto · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2506.15042

openalex publication_date 2025/06/18 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We generalize the equivariant intermediate Jacobian torsor obstruction over ℂ to algebraically closed fields of characteristic zero. It is an obstruction to the (projective) linearizability problem of finite group actions on threefolds. In addition, we calculate automorphism groups of general smooth Fano threefolds of No. 2.18. As an application, we prove that a general smooth Fano threefold X of No. 2.18 is linearizable for its automorphism group.

Citations

• Equivariant unirationality of Fano threefolds
• Linearization problem for finite subgroups of the plane Cremona group
• On the automorphism groups of smooth Fano threefolds
• Automorphisms of Fano threefolds of rank 2 and degree 28
• Equivariant geometry of singular cubic threefolds, II
• The K-moduli space of a family of conic bundle threefolds
• Reduction of Plane Quartics and Dixmier-Ohno invariants
• Equivariant geometry of singular cubic threefolds
• Equivariant geometry of the Segre cubic and the Burkhardt quartic
• K-stable Fano 3-folds in the families 2.18 and 3.4
• Equivariant birational geometry of linear actions
• Equivariant geometry of odd-dimensional complete intersections of two quadrics
• Stability and semi-stability of (2,2)-type surfaces
• Intermediate Jacobians and rationality over arbitrary fields
• Cycle class maps and birational invariants
• Rationality of complete intersections of two quadrics
• The moduli space of étale double covers of genus 5 curves is unirational
• Functoriality in resolution of singularities
• Finite subgroups of the plane Cremona group
• Lectures on Factorization of Birational Maps

Cited by

• Actions on the Picard group of smooth Fano threefolds

Related

• Intermediate Jacobians and linearizability
• Automorphisms of Fano threefolds of rank 2 and degree 28
• Equivariant geometry of singular cubic threefolds
• Equivariant rationality of Fano threefolds in the family \textnumero 2.12
• Fano threefolds of genus 6