$2$-nilpotent co-Higgs structures

Edoardo Ballico; Sukmoon Huh

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arXiv · 1606.02584

$2$-nilpotent co-Higgs structures

Edoardo Ballico·Sukmoon Huh

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Abstract

A co-Higgs sheaf is a pair of a torsion-free coherent sheaf $\mathcal{E}$ and a global section of $\mathcal{E}nd(\mathcal{E})\otimes T_X$ with $T_X$ the tangent bundle. We construct $2$-nilpotent co-Higgs sheaves of rank two for some rational surfaces and of rank three for $\mathbb{P}^3$, using the Hartshorne-Serre correspondence. Then we investigate the non-existence, specially over projective spaces.

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Edoardo Ballico, Sukmoon Huh. 2016-06-08. $2$-nilpotent co-Higgs structures. https://arxiv.org/abs/1606.02584

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