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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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
• Publisher: Springer
• ISSN: 1050-6926
• 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