{"paper":{"title":"On large theta-characteristics with prescribed vanishing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Edoardo Ballico, Francesco Bastianelli, Luca Benzo","submitted_at":"2015-07-28T06:50:01Z","abstract_excerpt":"Let $C$ be a smooth projective curve of genus $g\\geq 2$. Fix an integer $r\\geq 0$, and let $\\underline{k}=(k_1,\\ldots,k_n)$ be a sequence of positive integers with $k_1+\\ldots+k_n=g-1$. We study $n$-pointed curves $(C,p_1,\\ldots,p_n)$ such that the line bundle $L:=O_C\\left(\\sum_{i=1}^n k_i p_i\\right)$ is a theta-characteristic such that $h^0\\left(C,L\\right)$ is at least $r+1$ and it has the same parity as $r+1$. We prove that they describe a sublocus $\\mathcal{G}^r_g(\\underline{k})$ of $\\mathcal{M}_{g,n}$ having codimension at most $g-1+\\frac{r(r-1)}{2}$. Moreover, for any $r\\geq 0$, $\\underli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07665","kind":"arxiv","version":2},"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"}