Equations de Monge–Ampère dʹorigine géométrique sur certaines variétés algébriques

Résumé ve that the Monge–Ampère equation which is relative to the existence of Kähler–Einstein metricsLog M(ϕ)=−λϕ+fadmits, for allλ<(m+1)/4m, a solution on the blowing-up of the complex projective space of complex dimension m at one point. We establish the same result on the blowing-up of the two-dimentionnal projective space at two points, and this, for allλ<3/8.