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arXiv · 1912.05851

On the stability of tangent bundles on cyclic coverings

Yongming Zhang
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Abstract

Let $Y$ be a smooth projective surface defined over an algebraically closed field $k$ with ${\rm Char}\ k\nmid n$, and let $π:X\rightarrow Y$ be a $n$-cyclic covering branched along a smooth divisor $B$. We show that under some conditions $\mathscr{T}_X$ is semi-stable with respect to $π^*\mathcal {H}$ if the tangent bundle $\mathscr{T}_Y$ is semi-stable with respect to some ample line bundle $\mathcal {H}$ on $Y$.

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Yongming Zhang. 2019-12-12. On the stability of tangent bundles on cyclic coverings. https://arxiv.org/abs/1912.05851

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