{"paper":{"title":"The Hartpgs-type extension theorem for meromorphic mappings into q-complete complex spaces","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Alessandro Silva, Sergei Ivashkovich","submitted_at":"1998-10-28T10:30:11Z","abstract_excerpt":"We prove in this note a result on extension of meromorphic mappings, which can be considered as a direct generalisation of the Hartogs extension theorem for holomorphic functions. Namely:\n THEOREM. Every meromorphic mapping $f:H_n^q(r)\\to Y$, where $Y$ is a $q$ - -complete complex space, extends to a meromorphic mapping from $\\Delta^{n+q}$ to $Y$. Here $H_n^q(r):=\\Delta^n\\times (\\Delta^q\\setminus \\bar\\Delta_r^q)\\cup \\Delta_r^n\\times \\Delta^q$ is a \"q-concave\" Hartogs figure in $C^{n+q}$.\n Remark that in the case $q=1$, i.e. when $Y$ is Stein, the statement of the Theorem is exactly the Theorem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9810159","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"}