%0 Journal Article %T Monge-Ampere measures on subvarieties %A Per Ahag %A Urban Cegrell %A Pham Hoang Hiep %J Mathematics %D 2014 %I arXiv %X In this article we address the question whether the complex Monge-Amp\`{e}re equation is solvable for measures with large singular part. We prove that under some conditions there are no solution when the right-hand side is carried by a smooth subvariety in $\CEP{n}$ of dimension $k