2017/07/24 by Ruadhaí Dervan, Dervan, Ruadhaí, Lars Martin Sektnan +1
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP
paper · pdf · doi:10.48550/arxiv.1707.07638
23 pages. Final version, to appear in the Journal of Geometric Analysis
arxiv created 2019/09/26 · arxiv updated 2019/09/27
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 explict. This recovers, through the Hitchin-Kobayashi correspondence, algebro-geometric results due to Buchdahl and Sibley.