{"paper":{"title":"Estimates of the number of rational mappings from a fixed variety to varieties of general type","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"G. Dethloff, T. Bandman","submitted_at":"1996-08-29T13:39:45Z","abstract_excerpt":"First we find effective bounds for the number of dominant rational maps $f:X \\rightarrow Y$ between two fixed smooth projective varieties with ample canonical bundles. The bounds are of the type $\\{A \\cdot K_X^n\\}^{\\{B \\cdot K_X^n\\}^2}$, where $n=dimX$, $K_X$ is the canonical bundle of $X$ and $A,B $ are some constants, depending only on $n$. Then we show that for any variety $X$ there exist numbers $c(X)$ and $C(X)$ with the following properties: For any threefold $Y$ of general type the number of dominant rational maps $f:X \\r Y$ is bounded above by $c(X)$. The number of threefolds $Y$, modu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9608033","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"}