{"paper":{"title":"Linear syzygies and birational combinatorics","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Aron Simis, Rafael H. Villarreal","submitted_at":"2005-05-09T22:15:12Z","abstract_excerpt":"Let $F$ be a finite set of monomials of the same degree $d\\geq 2$ in a polynomial ring $R=k[x_1,...,x_n]$ over an arbitrary field $k$. We give some necessary and/or sufficient conditions for the birationality of the ring extension $k[F]\\subset R^{(d)}$, where $R^{(d)}$ is the $d${\\it th} Veronese subring of $R$. One of our results extends to arbitrary characteristic, in the case of rational monomial maps, a previous syzygy-theoretic birationality criterion in characteristic zero"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505159","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"}