Maximal disjoint Schubert cycles in rational homogeneous varieties

TL;DR

This paper investigates the structure of the Chow ring of rational homogeneous varieties, focusing on effective divisors and good divisibility, to understand the existence of nonconstant maps between these varieties.

Contribution

It generalizes previous results on projective spaces and Grassmannians to a broader class of rational homogeneous varieties by analyzing their Chow rings and divisibility properties.

Findings

Characterization of effective zero divisors of low codimension

Introduction of an invariant called effective good divisibility

Results on the (non)existence of nonconstant maps between varieties

Abstract

In this paper we study properties of the Chow ring of rational homogeneous varieties of classical type, more concretely, effective zero divisors of low codimension, and a related invariant called effective good divisibility. This information is then used to study the question of (non)existence of nonconstant maps among these varieties, generalizing previous results for projective spaces and Grassmannians.