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Genuinely ramified maps and stability of pulled-back parabolic bundles (2111.02313v2)

Published 3 Nov 2021 in math.AG

Abstract: Let $f : X \rightarrow Y$ be a genuinely ramified map between irreducible smooth projective curves defined over an algebraically closed field. Let $P$ be a branch data on $Y$ such that $P(y)$ and $B_f(y)$ where $B_f$ is branch data for $f$ are linearly disjoint for every $y \in, Y$. Further assume that either $P$ is tame or $f$ is Galois. Then the pullback, by $f$, of any stable parabolic bundle on $Y$ with respect to $P$ is actually a stable parabolic bundle on $X$ with respect to $f*P$.

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