Hermitian Yang-Mills connections on blowups

Ruadhaí Dervan; Lars Martin Sektnan

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arXiv · 1707.07638

Hermitian Yang-Mills connections on blowups

Ruadhaí Dervan·Lars Martin Sektnan

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Abstract

Consider a vector bundle over a K\"ahler manifold which admits a Hermitian Yang-Mills connection. We show that the pullback bundle on the blowup of the K\"ahler manifold at a collection of points also admits a Hermitian Yang-Mills connection, for K\"ahler 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.

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Ruadhaí Dervan, Lars Martin Sektnan. 2017-07-24. Hermitian Yang-Mills connections on blowups. https://arxiv.org/abs/1707.07638

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