On exterior powers of the tangent bundle on toric varieties

David Schmitz

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arXiv · 1811.02603

On exterior powers of the tangent bundle on toric varieties

David Schmitz

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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 $\Lambda^m\mathcal T_X$ in terms of wall relations. As an application, we classify smooth toric varieties of arbitrary dimension $n\ge3$ with $\Lambda^2\mathcal T_X$ nef and those of dimension $n\ge 4$ with $\Lambda^3\mathcal T_X$ ample.

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BibTeX RIS

David Schmitz. 2018-11-06. On exterior powers of the tangent bundle on toric varieties. https://arxiv.org/abs/1811.02603

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