Automorphisms of odd dimensional $(2,2)$-complete intersections in characteristic $2$

TL;DR

This paper computes the automorphism scheme of generic odd-dimensional (2,2)-complete intersections in characteristic 2, revealing a unique case with a non-trivial identity component among complete intersections.

Contribution

It identifies and analyzes the automorphism scheme of a specific class of complete intersections in characteristic 2, a case not previously well-understood.

Findings

Automorphism scheme computed for generic odd-dimensional (2,2)-complete intersections.

This is the only known case among complete intersections with a non-trivial identity component besides quadrics and genus 1 curves.

Provides new insights into automorphism structures in characteristic 2.

Abstract

We compute the automorphism scheme of a generic odd dimensional $(2,2)$-complete intersection in characteristic $2$. This is the only case for complete intersections having a non-trivial identity component in automorphism schemes apart from quadric hypersurfaces and genus $1$ curves.