{"paper":{"title":"Kaehler differentials for fat point schemes in P^1xP^1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Elena Guardo, Le Ngoc Long, Martin Kreuzer, Tran N. K. Linh","submitted_at":"2016-11-29T14:17:54Z","abstract_excerpt":"Let $X$ be a set of $K$-rational points in $P^1 \\times P^1$ over a field $K$ of characteristic zero, let $Y$ be a fat point scheme supported at $ X$, and let $R_Y$ be the bihomogeneus coordinate ring of $Y$. In this paper we investigate the module of Kaehler differentials $\\Omega^1_{R_Y/K}$. We describe this bigraded $R_Y$-module explicitly via a homogeneous short exact sequence and compute its Hilbert function in a number of special cases, in particular when the support $X$ is a complete intersection or an almost complete intersection in $P^1 \\times P^1$. Moreover, we introduce a Kaehler diff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09851","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"}