Ramified covering maps and stability of pulled back bundles

2021/02/17 by Biswas, Indranil, Parameswaran, A. J. · 1 citation
#14E20 #14H30 #14H60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.08744

Abstract

Let f:C→ 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→ C is stable for every stable vector bundle E on D if and only if f is genuinely ramified.

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