Direct image of parabolic line bundles |
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Authors: | Robert Auffarth Indranil Biswas |
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Affiliation: | 1. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Santiago, Chile;2. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India |
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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 a surjective étale morphism. The criterion in question is the existence of a Cartan subalgebra bundle of the endomorphism bundle . As a corollary, a criterion is obtained for E to be the direct image of the structure sheaf under an étale 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 the direct image of a parabolic line bundle under a ramified covering map. |
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Keywords: | 14E20 14J60 14L15 |
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