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EXTENSIONS OF VECTOR BUNDLES WITH APPLICATION TO NOETHER–LEFSCHETZ THEOREMS

    https://doi.org/10.1142/S021919971350003XCited by:5 (Source: Crossref)

    Given a smooth, projective variety Y over an algebraically closed field of characteristic zero, and a smooth, ample hyperplane section X ⊂ Y, we study the question of when a bundle E on X, extends to a bundle on a Zariski open set U ⊂ Y containing X. The main ingredients used are explicit descriptions of various obstruction classes in the deformation theory of bundles, together with Grothendieck–Lefschetz theory. As a consequence, we prove a Noether–Lefschetz theorem for higher rank bundles, which recovers and unifies the Noether–Lefschetz theorems of Joshi and Ravindra–Srinivas.

    AMSC: 14B10, 14C22, 14J60

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