{"paper":{"title":"Singular Kahler-Einstein metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Ahmed Zeriahi (IMT), Philippe Eyssidieux (IF), Vincent Guedj (LATP)","submitted_at":"2006-03-17T15:20:53Z","abstract_excerpt":"We study degenerate complex Monge-Amp\\`ere equations of the form $(\\omega+dd^c \\varphi)^n = e^{t \\varphi} \\mu$ where $\\omega$ is a big semi-positive form on a compact K\\\"ahler manifold $X$ of dimension $n$, $t \\in \\R^+$, and $\\mu=f\\omega^n$ is a positive measure with density $f\\in L^p(X,\\omega^n)$, $p>1$. We prove the existence and unicity of bounded $\\omega$-plurisubharmonic solutions. We also prove that the solution is continuous under a further technical condition.\n  In case $X$ is projective and $\\omega=\\psi^*\\omega'$, where $\\psi:X\\to V$ is a proper birational morphism to a normal project"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603431","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0603431/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}