Stability of tangent bundles on smooth toric Picard-rank-2 varieties and surfaces

2019/10/19 by Milena Hering, Hering, Milena, Benjamin Nill +3 · 2 citations
Mathematics · #14J60 (Primary) #14M25 (Secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.08848

openalex publication_date 2019/10/19 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We give a combinatorial criterion for the tangent bundle on a smooth toric variety to be stable with respect to a given polarisation in terms of the corresponding lattice polytope. Furthermore, we show that for a smooth toric surface and a smooth toric variety of Picard rank 2, there exists an ample line bundle with respect to which the tangent bundle is stable if and only if it is an iterated blow-up of projective space.

Cited by

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

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