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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

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Volume 2017, Issue 727

Issues

Complex Monge–Ampère equations on quasi-projective varieties

Eleonora Di Nezza / Chinh H. Lu
Published Online: 2014-09-26 | DOI: https://doi.org/10.1515/crelle-2014-0090

Abstract

We introduce generalized Monge–Ampère capacities and use these to study complex Monge–Ampère equations whose right-hand side is smooth outside a divisor. We prove, in many cases, that there exists a unique normalized solution which is smooth outside the divisor. Our results still hold if the divisor is replaced by any closed subset.

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About the article

Received: 2014-02-02

Revised: 2014-07-09

Published Online: 2014-09-26

Published in Print: 2017-06-01


The authors are partially supported by the French ANR project MACK. The second-named author is supported by the European Research Councils.


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2017, Issue 727, Pages 145–167, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2014-0090.

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