Hermitian Yang–Mills connections on blowups

Dervan, R. and Sektnan, L. M. (2021) Hermitian Yang–Mills connections on blowups. Journal of Geometric Analysis, 31(1), pp. 516-542. (doi: 10.1007/s12220-019-00286-0)

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Consider a vector bundle over a Kähler manifold which admits a Hermitian Yang–Mills connection. We show that the pullback bundle on the blowup of the Kähler manifold at a collection of points also admits a Hermitian Yang–Mills connection, for Kähler classes on the blowup which make the exceptional divisors small. Our proof uses gluing techniques, and is hence asymptotically explicit. This recovers, through the Hitchin–Kobayashi correspondence, algebro-geometric results due to Buchdahl and Sibley.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Dervan, Dr Ruadhaí
Authors: Dervan, R., and Sektnan, L. M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Geometric Analysis
ISSN (Online):1559-002X
Published Online:26 September 2019
Copyright Holders:Copyright © 2019 Mathematica Josephina, Inc.
First Published:First published in Journal of Geometric Analysis 31(1):516-542
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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