TL;DR
This paper explores the flexibility of Schubert classes in homogeneous varieties, providing constructions to represent multiples by irreducible subvarieties and strengthening existing theorems in the context of cominuscule varieties.
Contribution
It introduces new constructions for representing multiples of Schubert classes and improves upon previous results by showing all positive multiples of obstructed classes can be represented irreducibly.
Findings
Positive multiples of obstructed classes can be represented by irreducible subvarieties
Provides new methods for representing Schubert classes
Sharpens existing theorems on Schubert class representation
Abstract
In this note, we discuss the flexibility of Schubert classes in homogeneous varieties. We give several constructions for representing multiples of a Schubert class by irreducible subvarieties. We sharpen [R, Theorem 3.1] by proving that every positive multiple of an obstructed class in a cominuscule homogeneous variety can be represented by an irreducible subvariety.
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