A note on the canonical divisor of the generalised affine Stiefel algebraic varieties

TL;DR

This paper investigates the canonical divisor of generalized affine Stiefel algebraic varieties, a class of homogeneous spaces, by expressing it through group representations, extending known cases like affine Stiefel varieties and spheres.

Contribution

It provides a characterization of the canonical divisor for these varieties in terms of group representations, generalizing previous specific cases.

Findings

Canonical divisor expressed via group representations

Extension of known cases like affine Stiefel varieties and spheres

Provides a unified framework for these algebraic varieties

Abstract

In this paper we study certain homogeneous spaces, which we call generalised affine Stiefel algebraic varieties. The main aim is to characterise the canonical divisor of generalised affine Stiefel algebraic varieties in terms of group representations. Affine Stiefel algebraic varieties and in particular $S^{n}$ are two special cases of the generalised affine Stiefel algebraic varieties.