Invariant Gorenstein Rings On 3 Dimensional Spaces

TL;DR

This thesis classifies Gorenstein invariant rings in three variables under modular group actions, focusing on cases where the characteristic divides the group's order, advancing understanding in modular invariant theory.

Contribution

It provides a comprehensive classification of Gorenstein invariant rings in three variables for modular group actions, covering all cases of the G-module V.

Findings

Classification of Gorenstein invariant rings in modular case

Analysis of all G-module configurations for three variables

Detailed case-by-case study of group actions

Abstract

This is my master thesis, under the supervision of Professor Amiram Braun. We classify in these paper the Gorenstein invariant rings in the modular case, where the group that acts on the 3-variable polynomial ring is finite , and the Char (F)=p divides the order of this group. We divide our work into several cases that discuss all the situations of the G-module V, where V=span{x,y,z} is the space of the polynomial ring of three coefficients.