Ramified Covering Maps and Stability of Pulled-back Bundles
Ramified Covering Maps and Stability of Pulled-back Bundles
Abstract Let $f\,:\,C\,\longrightarrow \,D$ be a nonconstant separable morphism between irreducible smooth projective curves defined over an algebraically closed field. We say that $f$ is genuinely ramified if ${\mathcal O}_D$ is the maximal semistable subbundle of $f_*{\mathcal O}_C$ (equivalently, the induced homomorphism $f_*\,:\, \pi _1^{\textrm{et}}(C)\,\longrightarrow \, \pi _1^{\textrm{et}}(D)$ of étale …