Stable Higgs bundles on ruled surfaces
Stable Higgs bundles on ruled surfaces
Let $\pi : X = \mathbb{P}_C(E) \longrightarrow C$ be a ruled surface over an algebraically closed field $k$ of characteristic 0, with a fixed polarization $L$ on $X$. In this paper, we show that pullback of a (semi)stable Higgs bundle on $C$ under $\pi$ is a $L$-(semi)stable Higgs bundle. Conversely, …