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arXiv · 2112.00097

A Product Model for Generalizing Poincar\'e-Type K\"ahler Metrics

Ethan L Addison
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Abstract

We begin by defining a type of K\"ahler metric near the zero section of a trivial holomorphic open disk bundle $N$ over a compact K\"ahler manifold $X$ by incorporating flows generated by holomorphic vector fields on $X$. These metrics are then shown to deviate exponentially from Poincar\'e-type metrics on $N\setminus X$ in terms of the log-polar distance from $X$ in $N$. Lastly we see that they arise naturally when perturbing classes containing Poincar\'e-type K\"ahler metrics of constant scalar curvature to obtain nearby cscK metrics even when the perturbed class on $X$ does not admit a cscK metric.

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Ethan L Addison. 2021-11-30. A Product Model for Generalizing Poincar\'e-Type K\"ahler Metrics. https://arxiv.org/abs/2112.00097

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