Descent of varieties using a Groebner basis argument

TL;DR

This paper establishes a descent theorem for affine and projective varieties over algebraically closed fields by analyzing the behavior of reduced Groebner bases under automorphism group actions.

Contribution

It introduces a novel approach using Groebner bases to study descent of varieties via automorphism group actions.

Findings

Proves a descent theorem for varieties over algebraically closed fields.

Utilizes Groebner basis properties to analyze automorphism group actions.

Provides a new method for understanding the descent of algebraic varieties.

Abstract

We prove a descent result for affine/projective varieties defined over an algebraically closed field. The idea is to work with the reduced Groebner basis of the ideal where the variety vanishes and study it's behaviour under group action coming from subgroups of the automorphism group of the base field.