On exterior powers of the tangent bundle on toric varieties

2018/11/06 by David Schmitz, Schmitz, David · 1 citation
Mathematics · Physics and Astronomy · #14J60 #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1811.02603

openalex publication_date 2018/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the positivity of exterior powers of the tangent sheaf on toric varieties in order to generalize results by Campana and Peternell about 3-folds with nef second exterior power of the tangent bundle. Using the theory of equivariant vector bundles and the toric MMP, we establish in the smooth case a criterion for the positivity of Λ^m\mathcal T_X in terms of wall relations. As an application, we classify smooth toric varieties of arbitrary dimension n≥3 with Λ²\mathcal T_X nef and those of dimension n≥ 4 with Λ³\mathcal T_X ample.

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• Positivity of the second exterior power of the tangent bundles

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