Automorphism and Cohomology I: Fano variety of lines and Cubic

2015/11/17 by Xuanyu Pan, Pan, Xuanyu
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1511.05272

openalex publication_date 2015/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a general principle of lifting an automorphism from positive characteristic to zero characteristic. We based on the principle to prove the automorphism group of Fano variety of cubic threefold (fourfold) acts on its cohomology group faithfully. We also prove the same result for a singular cubic threefold (fourfold) with one ordinary double singularity. As an application, we classify the automorphism groups of cubic fourfolds with small middle Picard number over complex numbers.

Related

• The Fano variety of lines of a cuspidal cyclic cubic fourfold
• The Fano variety of lines on singular cyclic cubic fourfolds
• Liftability and vanishing theorems for Fano threefolds in positive characteristic II
• Actions on the Picard group of smooth Fano threefolds
• Automorphisms of Fano threefolds of rank 2 and degree 28