{"paper":{"title":"Lower bounds for Waldschmidt constants of generic lines in $\\mathbb{P}^3$ and a Chudnovsky-type theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Halszka Tutaj-Gasinska, Justyna Szpond, Marcin Dumnicki, Mohammad Zaman Fashami","submitted_at":"2018-03-06T19:14:05Z","abstract_excerpt":"The Waldschmidt constant $\\alphahat(I)$ of a radical ideal $I$ in the coordinate ring of $\\PP^N$ measures (asymptotically) the degree of a hypersurface passing through the set defined by $I$ in $\\PP^N$. Nagata's approach to the 14th Hilbert Problem was based on computing such constant for the set of points in $\\PP^2$. Since then, these constants drew much attention, but still there are no methods to compute them (except for trivial cases). Therefore the research focuses on looking for accurate bounds for $\\alphahat(I)$.\n  In the paper we deal with $\\alphahat(s)$, the Waldschmidt constant for $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02387","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"}