{"paper":{"title":"On the density function on moduli spaces of toric 4-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.SG","authors_text":"Alessio Figalli, \\'Alvaro Pelayo","submitted_at":"2014-08-07T02:03:21Z","abstract_excerpt":"The optimal density function assigns to each symplectic toric manifold $M$ a number $0 < d \\leq 1$ obtained by considering the ratio between the maximum volume of $M$ which can be filled by symplectically embedded disjoint balls and the total symplectic volume of $M$. In the toric version of this problem, $M$ is toric and the balls need to be embedded respecting the toric action on $M$. The goal of this note is first to give a brief survey of the notion of toric symplectic manifold and the recent constructions of moduli space structure on them, and recall how to define a natural density functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1462","kind":"arxiv","version":3},"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"}