KASS seminar

Abstract: In joint work in progress with Mats Andersson, we study Segre and Chern forms associated to singular metrics on vector bundles. The metrics we consider are in a suitable sense quasiplurisubharmonic with analytic singularities, inspired by the case of so-called Griffiths negatively curved metrics on vector bundles, which corresponds to smooth plurisubharmonic metrics. The forms are in fact currents, more precisely a type of currents that we introduce, quasi-cycles, which contain integration currents along subvarieties, as well as Bedford-Taylor type Monge-Ampère products. Our results extend previous results about such Segre and Chern forms, and in particular, we obtain new results about their Lelong numbers, and a new natural regularization of them.