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arXiv · 1802.06614

Chern forms of hermitian metrics with analytic singularities on vector bundles

Richard Lärkäng·Hossein Raufi·Martin Sera·Elizabeth Wulcan
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Abstract

We define Chern and Segre forms, or rather currents, associated with a Griffiths positive singular hermitian metric $h$ with analytic singularities on a holomorphic vector bundle $E$. The currents are constructed as pushforwards of generalized Monge-Amp\`ere products on the projectivization of $E$. The Chern and Segre currents represent the Chern and Segre classes of $E$, respectively, and coincide with the Chern and Segre forms of $E$ and $h$, where $h$ is smooth. Moreover, our currents coincide with the Chern and Segre forms constructed by the first three authors and Ruppenthal in the cases when these are defined.

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Richard Lärkäng, Hossein Raufi, Martin Sera, Elizabeth Wulcan. 2018-02-19. Chern forms of hermitian metrics with analytic singularities on vector bundles. https://doi.org/10.1512/iumj.2022.71.8834

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