Minuscule Schubert Varieties of Exceptional Type

TL;DR

This paper investigates exceptional minuscule Schubert varieties, providing their defining equations, resolutions, and characterizations, thereby advancing understanding of their algebraic structure and Gorenstein properties.

Contribution

It offers explicit defining equations and resolutions for these varieties, linking them to fundamental Gorenstein ideals, which is a novel contribution.

Findings

Explicit defining equations for exceptional minuscule Schubert varieties.

Resolutions of their defining ideals are constructed.

Characterization of some ideals as fundamental Gorenstein ideals.

Abstract

We study exceptional minuscule Schubert varieties and provide the defining equations of the defining ideals of their intersection with the big open cell. We also provide the resolutions of these ideals and characterize some of them in terms of fundamental examples of ideals in the theory of Gorenstein ideals.