The Fano variety of lines of a cuspidal cyclic cubic fourfold

TL;DR

This paper investigates the geometric and automorphic properties of the Fano variety of lines on a cuspidal cyclic cubic fourfold, revealing its symplectic structure, singularities, and automorphism behavior.

Contribution

It demonstrates that the Fano variety is a symplectic variety with A2-singularities and analyzes the induced automorphism on the resolved holomorphic symplectic manifold.

Findings

Fano variety has transversal A2-singularities

Induced automorphism is of nonsymplectic order three

The variety admits a symplectic structure with specific singularities

Abstract

We prove that the Fano variety of lines of a cuspidal cyclic cubic fourfold is a symplectic variety with transversal A2-singularities and we study the properties of the nonsymplectic order three automorphism induced by the covering automorphism on the irreducible holomorphic symplectic manifold obtained by blowing up the singular locus.