{"paper":{"title":"Hemisystems of the Hermitian Surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"G\\'abor Korchm\\'aros, G\\'abor P. Nagy, Pietro Speziali","submitted_at":"2017-10-17T15:05:42Z","abstract_excerpt":"We present a new method for the study of hemisystems of the Hermitian surface $\\mathcal{U}_3$ of $PG(3,q^2)$. The basic idea is to represent generator-sets of $\\mathcal{U}_3$ by means of a maximal curve naturally embedded in $\\mathcal{U}_3$ so that a sufficient condition for the existence of hemisystems may follow from results about maximal curves and their automorphism groups. In this paper we obtain a hemisystem in $\\ PG(3,p^2)$ for each $p$ prime of the form $p=1+16n^2$ with an integer $n$. Since the famous Landau's conjecture dating back to 1904 is still to be proved (or disproved), it is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06335","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"}