{"paper":{"title":"A remark on the intersection of plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"C. Ciliberto, F. Flamini, M. Zaidenberg","submitted_at":"2017-04-02T15:52:41Z","abstract_excerpt":"Let $D$ be a very general curve of degree $d=2\\ell-\\epsilon$ in $\\mathbb{P}^2$, with $\\epsilon\\in \\{0,1\\}$. Let $\\Gamma \\subset \\mathbb{P}^2$ be an integral curve of geometric genus $g$ and degree $m$, $\\Gamma \\neq D$, and let $\\nu: C\\to \\Gamma$ be the normalization. Let $\\delta$ be the degree of the \\emph{reduction modulo 2} of the divisor $\\nu^*(D)$ of $C$. In this paper we prove the inequality $4g+\\delta\\geqslant m(d-8+2\\epsilon)+5$. We compare this with similar inequalities due to Geng Xu and Xi Chen. Besides, we provide a brief account on genera of subvarieties in projective hypersurfaces"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00320","kind":"arxiv","version":4},"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"}