Singular Kahler-Einstein metrics
| dc.creator | Eyssidieux, Philippe | |
| dc.creator | Guedj, Vincent | |
| dc.creator | Zeriahi, Ahmed | |
| dc.date | 2006-03-17 | |
| dc.date | 2008-09-24 | |
| dc.date.accessioned | 2026-07-07T10:04:44Z | |
| dc.date.available | 2026-07-07T10:04:44Z | |
| dc.description | We study degenerate complex Monge-Ampère equations of the form $(ω+dd^c φ)^n = e^{t φ} μ$ where $ω$ is a big semi-positive form on a compact Kähler manifold $X$ of dimension $n$, $t \in \R^+$, and $μ=fω^n$ is a positive measure with density $f\in L^p(X,ω^n)$, $p>1$. We prove the existence and unicity of bounded $ω$-plurisubharmonic solutions. We also prove that the solution is continuous under a further technical condition. In case $X$ is projective and $ω=ψ^*ω'$, where $ψ:X\to V$ is a proper birational morphism to a normal projective variety, $[ω']\in NS_{\R} (V)$ is an ample class and $μ$ has only algebraic singularities, we prove that the solution is smooth in the regular locus of the equation. We use these results to construct singular Kähler-Einstein metrics of non-positive curvature on projective klt pairs, in particular on canonical models of algebraic varieties of general type. | |
| dc.description | To appear in Journal of A.M.S | |
| dc.identifier | https://arxiv.org/abs/math/0603431 | |
| dc.identifier | http://arxiv.org/abs/math/0603431 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169784 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 32W20, 32Q20, 32J27, 14J17 | |
| dc.title | Singular Kahler-Einstein metrics | |
| dc.type | text |