EXTENSIONS OF VECTOR BUNDLES WITH APPLICATION TO NOETHER-LEFSCHETZ THEOREMS

作者：Ravindra G V^*; Tripathi Amit

来源：Communications in Contemporary Mathematics, 2013, 15(5): UNSP 1350003.

DOI：10.1142/S021919971350003X

• Vector bundles
• algebraic varieties
• extensions of bundles
• Noether-Lefschetz theorem

Given a smooth, projective variety Y over an algebraically closed field of characteristic zero, and a smooth, ample hyperplane section X subset of Y, we study the question of when a bundle E on X, extends to a bundle epsilon on a Zariski open set U subset of 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.

• 出版日期2013-10