{"paper":{"title":"Demailly's conjecture on Waldschmidt constants for sufficiently many very general points in $\\mathbb{P}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Shin-Yao Jow, Yu-Lin Chang","submitted_at":"2019-03-14T06:00:18Z","abstract_excerpt":"Let $Z$ be a finite set of $s$ points in the projective space $\\mathbb{P}^n$ over an algebraically closed field $F$. For each positive integer $m$, let $\\alpha(mZ)$ denote the smallest degree of nonzero homogeneous polynomials in $F[x_0,\\ldots,x_n]$ that vanish to order at least $m$ at every point of $Z$. The Waldschmidt constant $\\widehat{\\alpha}(Z)$ of $Z$ is defined by the limit \\[\n  \\widehat{\\alpha}(Z)=\\lim_{m \\to \\infty}\\frac{\\alpha(mZ)}{m}. \\] Demailly conjectured that \\[ \\widehat{\\alpha}(Z)\\geq\\frac{\\alpha(mZ)+n-1}{m+n-1}. \\] Recently, Malara, Szemberg, and Szpond established Demailly's"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05824","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"}