Automorphism and Cohomology I: Fano variety of lines and Cubic

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.

We remove the parts about crystalline cohomology and cite the main result in the section about crystalline cohomology with a reference

Cited by in corpus (4)

• Automorphism and Cohomology II: Complete intersections
• Surfaces of general type with q=2 are rigidified
• Jordan constant for Cremona group of rank 3
• Remarks on Automorphism and Cohomology of Cyclic Coverings