{"paper":{"title":"On the lifting problem in $\\mathbb P^4$ in characteristic $p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Paola Bonacini","submitted_at":"2011-09-08T15:06:26Z","abstract_excerpt":"Given $\\mathbb P^4_k$, with $k$ algebraically closed field of characteristic $p>0$, and $X\\subset \\mathbb P^4_k$ integral surface of degree $d$, let $Y=X\\cap H$ be the general hyperplane section of $X$. We suppose that $h^0\\mathscr I_Y(s)\\ne 0$ and $h^0\\mathscr I_X(s)=0$ for some $s>0$. This determines a nonzero element $\\alpha\\in H^1\\mathscr I_X(s)$ such that $\\alpha\\cdot H=0$ in $H^1\\mathscr I_X(s)$. We find different upper bounds of $d$ in terms of $s$, $p$ and the order of $\\alpha$ and we show that these bounds are sharp. In particular, we see that $d\\le s^2$ for $p<s$ and $d\\le s^2-s+2$ f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1738","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"}