Complex Monge-Ampère equations on quasi-projective varieties

Journal article, 2017

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.