On the stability of tangent bundles on cyclic coverings

Abstract

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

8 pages

References in corpus (1)

• Direct images of bundles under Frobenius morphisms