Order on the Fixed Points of the Gieseker Variety With Respect to the Torus Action

TL;DR

This paper investigates three families of orders on multipartitions, focusing on a geometric order on fixed points of the Gieseker variety under a torus action, and compares it with two bounding orders.

Contribution

It introduces and analyzes a geometric order on fixed points of the Gieseker variety, providing bounds and an almost precise description of this order.

Findings

The geometric order is closely approximated by two bounding orders.

The orders depend on r rational parameters and relate to multipartitions.

Provides a new perspective on fixed points in Gieseker varieties.

Abstract

In this paper I consider three families of orders on the set of r- multipartitions of n, depending on r rational parameters. The one we are interested in is a geometric order on the set of fixed points for a torus action on the Gieseker variety. The other two serve as bounds for the geometric one, providing an almost accurate description.