Stable equivariant birationalities of cubic and degree 14 Fano threefolds

TL;DR

This paper introduces an equivariant approach to birational geometry, establishing new stable birational equivalences between cubic threefolds and degree 14 Fano threefolds using the Pfaffian-Grassmannian correspondence.

Contribution

It develops an equivariant version of the Pfaffian-Grassmannian correspondence and applies it to find nontrivial twisted equivariant stable birationalities between specific threefolds.

Findings

Established equivariant stable birationalities between cubic and degree 14 Fano threefolds

Developed an equivariant version of the Pfaffian-Grassmannian correspondence

Provided explicit examples of nontrivial twisted equivariant birationalities

Abstract

We develop an equivariant version of the Pfaffian-Grassmannian correspondence and apply it to produce examples of nontrivial twisted equivariant stable birationalities between cubic threefolds and degree 14 Fano threefolds.