Semi-stability and local wall-crossing for hermitian Yang-Mills connections

Andrew Clarke; Carl Tipler

Semi-stability and local wall-crossing for hermitian Yang-Mills connections

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arxiv 2304.05245 v1 pith:DT2LV36A submitted 2023-04-11 math.DG math.AG

Andrew Clarke , Carl Tipler This is my paper · ORCID

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keywords ahlerconnectionsgradedobjectpolarisationabelianassociatedassuming

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We consider a sufficiently smooth semi-stable holomorphic vector bundle over a compact K\"ahler manifold. Assuming the automorphism group of its graded object to be abelian, we provide a semialgebraic decomposition of a neighbourhood of the polarisation in the K\"ahler cone into chambers characterising (in)stability. For a path in a stable chamber converging to the initial polarisation, we show that the associated HYM connections converge to an HYM connection on the graded object.

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