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arXiv · 2102.08744

Ramified covering maps and stability of pulled back bundles

Indranil Biswas·A. J. Parameswaran
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Abstract

Let $f:C\rightarrow D$ 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 homomorphism of etale fundamental groups is surjective). We prove that the pullback $f^*E\rightarrow C$ is stable for every stable vector bundle $E$ on $D$ if and only if $f$ is genuinely ramified.

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BibTeXRIS

Indranil Biswas, A. J. Parameswaran. 2021-02-17. Ramified covering maps and stability of pulled back bundles. https://arxiv.org/abs/2102.08744

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