Complex Monge-Amp\`ere equations on quasi-projective varieties
  We introduce generalized Monge-Amp\`ere capacities and use these to study complex Monge-Amp\`ere 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. 
Eleonora Di Nezza and Chinh H. Lu
math.CV math.AP math.DG