A note on stable toric sheaves of low rank

2023/07/06 by Tipler, Carl · 2 citations
#14M25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.02822

Abstract

Kaneyama and Klyachko have shown that any torus equivariant vector bundle of rank r over \mathbbCPⁿ splits if r < n. In particular, any such bundle is not slope stable. In contrast, we provide explicit examples of stable equivariant reflexive sheaves of rank r on any polarised toric variety (X, L), for 2 ≤ r < dim(X) + rank(Pic(X)), and show that the dimension of their singular locus is strictly bounded by n - r.

Cited by

• Stable toric sheaves. I : Chern classes
• Polynomial stability conditions for vector bundles: Positivity, equivariance and blow-ups

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