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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1507.07665","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-28T06:50:01Z","cross_cats_sorted":[],"title_canon_sha256":"dbb11be1485caf85cab0d3a882c56eddb86c6edb1124e9268ab219e4187027dd","abstract_canon_sha256":"c5c6d5a0f9833600b327f588ce84c10896acf3a237ebaed36627f215ba523588"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:07.770281Z","signature_b64":"lu1+6Nan2H5WtDwboi0Bzm4B4Nx8Ju/7hqEDIMMECnli6lEYN6Va1JtDxgVbIrig8BNkyRIqdkhVDcDv7wUhAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7b3c6c469ad99bab72254d66ecc33245442705669d418e32cbbbda427bda1bd","last_reissued_at":"2026-05-18T01:32:07.769497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:07.769497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1507.07665","created_at":"2026-05-18T01:32:07.769633+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.07665v2","created_at":"2026-05-18T01:32:07.769633+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07665","created_at":"2026-05-18T01:32:07.769633+00:00"},{"alias_kind":"pith_short_12","alias_value":"U6Z4NRDJVWM3","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"U6Z4NRDJVWM3VNZC","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"U6Z4NRDJ","created_at":"2026-05-18T12:29:44.643036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U6Z4NRDJVWM3VNZCKTLG5TBTER","json":"https://pith.science/pith/U6Z4NRDJVWM3VNZCKTLG5TBTER.json","graph_json":"https://pith.science/api/pith-number/U6Z4NRDJVWM3VNZCKTLG5TBTER/graph.json","events_json":"https://pith.science/api/pith-number/U6Z4NRDJVWM3VNZCKTLG5TBTER/events.json","paper":"https://pith.science/paper/U6Z4NRDJ"},"agent_actions":{"view_html":"https://pith.science/pith/U6Z4NRDJVWM3VNZCKTLG5TBTER","download_json":"https://pith.science/pith/U6Z4NRDJVWM3VNZCKTLG5TBTER.json","view_paper":"https://pith.science/paper/U6Z4NRDJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.07665&json=true","fetch_graph":"https://pith.science/api/pith-number/U6Z4NRDJVWM3VNZCKTLG5TBTER/graph.json","fetch_events":"https://pith.science/api/pith-number/U6Z4NRDJVWM3VNZCKTLG5TBTER/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U6Z4NRDJVWM3VNZCKTLG5TBTER/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U6Z4NRDJVWM3VNZCKTLG5TBTER/action/storage_attestation","attest_author":"https://pith.science/pith/U6Z4NRDJVWM3VNZCKTLG5TBTER/action/author_attestation","sign_citation":"https://pith.science/pith/U6Z4NRDJVWM3VNZCKTLG5TBTER/action/citation_signature","submit_replication":"https://pith.science/pith/U6Z4NRDJVWM3VNZCKTLG5TBTER/action/replication_record"}},"created_at":"2026-05-18T01:32:07.769633+00:00","updated_at":"2026-05-18T01:32:07.769633+00:00"}