Hilbert Schemes with Two Borel-fixed Points in Arbitrary Characteristic

TL;DR

This paper generalizes the classification of Hilbert schemes with two Borel-fixed points to all characteristics by combining Reeves' algorithm with properties of Borel-fixed ideals and prior classifications.

Contribution

It extends existing classifications to arbitrary characteristic using a synthesis of algorithms and theoretical properties.

Findings

Classification of Hilbert schemes with two Borel-fixed points in any characteristic

Integration of Reeves' algorithm with properties of Borel-fixed ideals

Complete characterization of these schemes in arbitrary characteristic

Abstract

We extend the recent classification of Hilbert schemes with two Borel-fixed points to arbitrary characteristic. We accomplish this by synthesizing Reeves' algorithm for generating strongly stable ideals with the basic properties of Borel-fixed ideals and our previous work classifying Hilbert schemes with unique Borel-fixed points.