• Vector bundles as direct images of line bundles

• # Fulltext

Permanent link:
https://www.ias.ac.in/article/fulltext/pmsc/104/01/0191-0200

• # Keywords

Projective variety; algebraic vector bundle; line bundle; direct image; finite morphism

• # Abstract

LetX be a smooth irreducible projective variety over an algebraically closed fieldK andE a vector bundle onX. We prove that, if dimX ≥ 1, there exist a smooth irreducible projective varietyZ overK, a surjective separable morphismf:ZX which is finite outside an algebraic subset of codimension ≥ 3 inX and a line bundleL onX such that the direct image ofL byf is isomorphic toE. WhenX is a curve, we show thatZ, f, L can be so chosen thatf is finite and the canonical mapH1(Z, O) →H1(X, EndE) is surjective.

• # Author Affiliations

1. Université de Nice Sophia-Antipolis, Parc Valrose, Nice Cedex 2 - 06108, France
2. International Centre for Theoretical Physics, P.O. Box 586, Trieste - 34100, Italy

• # Proceedings – Mathematical Sciences

Volume 131, 2021
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• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019

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