Density of positive closed currents, a theory of non-generic intersections

Dinh, Tien-Cuong; Sibony, Nessim

doi:10.1090/jag/711

Authors: Tien-Cuong Dinh and Nessim Sibony
Journal: J. Algebraic Geom. 27 (2018), 497-551
DOI: https://doi.org/10.1090/jag/711
Published electronically: March 30, 2018
MathSciNet review: 3803606
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Abstract | References | Additional Information

Abstract: We introduce a notion of density which extends both the notion of the Lelong number and the theory of intersection for positive closed currents on Kähler manifolds. For an arbitrary finite family of positive closed currents on a compact Kähler manifold we construct cohomology classes which represent their intersection even when a phenomenon of dimension excess occurs. An example is the case of two algebraic varieties whose intersection has dimension larger than the expected number. The theory allows us to solve problems in complex dynamics. Basic calculus on the density of currents is established.

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Additional Information

Tien-Cuong Dinh
Affiliation: Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076
MR Author ID: 608547
Email: matdtc@nus.edu.sg

Nessim Sibony
Affiliation: Université Paris-Sud, Mathématique - Bâtiment 425, 91405 Orsay, France
MR Author ID: 161495
Email: nessim.sibony@math.u-psud.fr

Received by editor(s): November 13, 2015
Received by editor(s) in revised form: December 26, 2016, and July 18, 2017
Published electronically: March 30, 2018
Article copyright: © Copyright 2018 University Press, Inc.