Advances in Theoretical and Mathematical Physics

Volume 20 (2016)

Number 2

The Calabi–Yau theorem and Kähler currents

Pages: 381 – 404

DOI: http://dx.doi.org/10.4310/ATMP.2016.v20.n2.a4

Author

Valentino Tosatti (Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.)

Abstract

In this note we give an overview of some applications of the Calabi–Yau theorem to the construction of singular positive $(1, 1)$ currents on compact complex manifolds. We show how recent developments allow us to give streamlined proofs of existing results, as well as new ones.

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