Direct image of parabolic line bundles

Robert Auffarth; Indranil Biswas

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arXiv · 1612.04013

Direct image of parabolic line bundles

Robert Auffarth·Indranil Biswas

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Abstract

Given a vector bundle $E$ on an irreducible projective variety $X$ we give a necessary and sufficient criterion for $E$ to be a direct image of a line bundle under an \'etale morphism. The criterion in question is the existence of a Cartan subalgebra bundle of the endomorphism bundle $\text{End}(E)$. As a corollary, a criterion is obtained for $E$ to be the direct image of the structure sheaf under an \'etale morphism. The direct image of a parabolic line bundle under any ramified covering map has a natural parabolic structure. Given a parabolic vector bundle, we give a similar criterion for it to be a direct image of a parabolic line bundle under a ramified covering map.

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BibTeX RIS

Robert Auffarth, Indranil Biswas. 2016-12-13. Direct image of parabolic line bundles. https://arxiv.org/abs/1612.04013

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