{"paper":{"title":"Pseudo-isomorphisms in dimension $3$ and applications to complex Monge-Ampere equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Tuyen Trung Truong","submitted_at":"2014-03-20T19:14:48Z","abstract_excerpt":"Let $X$ and $Y$ be compact K\\\"ahler manifolds of dimension $3$. A bimeromorphic map $f:X\\rightarrow Y$ is pseudo-isomorphic if $f:X-I(f)\\rightarrow Y-I(f^{-1})$ is an isomorphism.\n  In this paper we investigate some properties of pseudo-isomorphisms. As an application, we associate to any pseudo-isomorphism in dimension $3$ and a smooth closed $(3,3)$ form $\\delta$ on $X\\times X$ representing the cohomology class of the diagonal $\\Delta_X$, a Monge-Ampere operator $MA(f^*(\\theta),\\delta)=f^*(\\theta)\\wedge f^*(\\theta)\\wedge f^*(\\theta)$, here $\\theta$ is a smooth closed $(1,1)$ form on $Y$. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5235","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":""},"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"}