Loss of mass of non-pluripolar products

Duc-Viet Vu

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arXiv · 2101.05483

Loss of mass of non-pluripolar products

Duc-Viet Vu

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Abstract

It is a well-known fact that the non-pluripolar self-products of a closed positive (1,1)-current in a big nef cohomology class on a compact Kahler manifold are not of full mass in the presence of positive Lelong numbers of the current in consideration. In this paper, we give a quantitative version of the last property. Our proof involves a generalization of Demailly's comparison of Lelong numbers to the setting of density currents, a reversed Alexandrov-Fenchel inequality, and the notion of relative non-pluripolar products.

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Duc-Viet Vu. 2021-01-14. Loss of mass of non-pluripolar products. https://arxiv.org/abs/2101.05483

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