{"paper":{"title":"The simplicity of the first spectral radius of a meromorphic map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.DS","authors_text":"Tuyen Trung Truong","submitted_at":"2012-12-05T16:31:48Z","abstract_excerpt":"Let $X$ be a compact K\\\"ahler manifold and let $f:X\\rightarrow X$ be a dominant rational map which is 1-stable. Let $\\lambda_1$ and $\\lambda_2$ be the first and second dynamical degrees of $f$. If $\\lambda_1^2>\\lambda_2$, then we show that $\\lambda_1$ is a simple eigenvalue of $f^*:H^{1,1}(X)\\rightarrow H^{1,1}(X)$, and moreover the unique eigenvalue of modulus $>\\sqrt{\\lambda_2}$. A variant of the result, where we consider the first spectral radius in the case the map $f$ may not be 1-stable, is also given. An application is stated for bimeromorphic selfmaps of 3-folds.\n  In the last section "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1091","kind":"arxiv","version":1},"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"}