{"paper":{"title":"On the Hilbert function on $\\mathbb P^1\\times\\mathbb P^1$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Lucia Marino, Paola Bonacini","submitted_at":"2010-09-21T13:50:29Z","abstract_excerpt":"Let $Q = \\mathbb P^1 x \\mathbb P^1$ and let $X\\subset Q$ be a 0-dimensional scheme. This paper is a first step towards the characterization of Hilbert functions of 0- dimensional schemes in $Q$. In particular we show how, under some conditions on $X$, its Hilbert function changes when we add points to $X$ lying on a $(1,0)$ or $(0, 1)$-line. As a particular case we show also that if $X$ is ACM this result holds without any additional hypothesis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4095","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"}