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arXiv · 1907.01386

On a mixed Monge-Amp\`ere operator for quasiplurisubharmonic functions with analytic singularities

Richard Lärkäng·Martin Sera·Elizabeth Wulcan
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Abstract

We consider mixed Monge-Amp\`ere products of quasiplurisubharmonic functions with analytic singularities, and show that such products may be regularized as explicit one parameter limits of mixed Monge-Amp\`ere products of smooth functions, generalizing results of Andersson, B{\l}ocki and the last author in the case of non-mixed Monge-Amp\`ere products. Connections to the theory of residue currents, going back to Coleff-Herrera, Passare and others, play an important role in the proof. As a consequence we get an approximation of Chern and Segre currents of certain singular hermitian metrics on vector bundles by smooth forms in the corresponding Chern and Segre classes.

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Richard Lärkäng, Martin Sera, Elizabeth Wulcan. 2019-07-02. On a mixed Monge-Amp\`ere operator for quasiplurisubharmonic functions with analytic singularities. https://doi.org/10.1112/blms.12307

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