Equivariant geometry of the Segre cubic and the Burkhardt quartic

TL;DR

This paper investigates the symmetries of the Segre cubic and Burkhardt quartic using advanced algebraic geometry and group theory techniques to understand their linearization properties.

Contribution

It introduces new methods to analyze group actions on these complex algebraic varieties, combining cohomology, birational rigidity, and Burnside formalism.

Findings

Criteria for linearizability of group actions established

Identification of conditions for stable linearizability

Enhanced understanding of symmetry properties of the varieties

Abstract

We study linearizability and stable linearizability of actions of finite groups on the Segre cubic and Burkhardt quartic, using techniques from group cohomology, birational rigidity, and the Burnside formalism.