An extension theorem for Hermitian line bundles. (English) Zbl 1382.32007

Aryasomayajula, Anilatmaja (ed.) et al., Analytic and algebraic geometry. Selected papers based on the presentations at the international conference, Hyderabad, India 2015. New Delhi: Hindustan Book Agency (ISBN 978-93-86279-64-4/hbk). 225-237 (2017).
Let \(Y\) be a reduced complex space and \(A\) a closed complex analytic subspace. Let \((L, h)\) be a holomorphic Hermitian line bundle on the complement of \(A\) such that the curvature of the Chern connection is positive. Assume that there is a desingularization of \(Y\) such that this curvature extends as a positive current. Then the main theorem asserts that there is a modification of \(Y\) which is an isomorphism over the complement of \(A\) and \((L, h)\) extends to it as a holomorphic line bundle with a singular Hermitian metric whose curvature is a positive current. Some applications of it are given in the context of the Quillen determinant line bundle. This paper is well written.
For the entire collection see [Zbl 1377.14003].


32C15 Complex spaces
32L05 Holomorphic bundles and generalizations
32D15 Continuation of analytic objects in several complex variables
Full Text: DOI arXiv