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arXiv · 2210.15342

Non-pluripolar products on vector bundles and Chern--Weil formulae

Mingchen Xia
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Abstract

In this paper, we develop several pluripotential-theoretic techniques for singular metrics on vector bundles. We first introduce the theory of non-pluripolar products on holomorphic vector bundles on complex manifolds. Then we define and study a special class of singularities of Hermitian metrics on vector bundles, called $\mathcal{I}$-good singularities, partially extending Mumford's notion of good singularities. Next, we derive a Chern--Weil type formula expressing the Chern numbers of Hermitian vector bundles with $\mathcal{I}$-good singularities in terms of the associated b-divisors. We also define an intersection theory on the Riemann--Zariski space and apply it to reformulate our Chern--Weil formula.

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BibTeXRIS

Mingchen Xia. 2022-10-27. Non-pluripolar products on vector bundles and Chern--Weil formulae. https://arxiv.org/abs/2210.15342

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