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As applications, we determine all theta divisors that are dominated by a product of curves and characterize Jacobians by the existence of a d-dimensional subvariety with curve summand whose twisted ideal sheaf is a generic vanishing sheaf."},"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":"1409.3134","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-10T16:10:22Z","cross_cats_sorted":[],"title_canon_sha256":"8384c73c1ea7a4e4f946baf61d48277a5c190432a34bffd11fd6546313fa48c1","abstract_canon_sha256":"a47b26c7c4dba454d7ca517b88a09e6f06864eca51e2dbbcfe78d8e6994bae6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:02.492199Z","signature_b64":"1rpENgVq2b9Lx3/Nfk3yncvDSICAq1leop02gbxr1rFh8BzbVcQQpXQEcWOB+16oy6/5H4iY3YJsGeuv0dd9Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24d7b2c7bd6e4a84a8ad3fcde890a9ce2de738c8de11cfc2e80a5dbf8176e667","last_reissued_at":"2026-05-18T00:02:02.491706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:02.491706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Theta divisors with curve summands and the Schottky problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Stefan Schreieder","submitted_at":"2014-09-10T16:10:22Z","abstract_excerpt":"We prove the following converse of Riemann's Theorem: let (A,\\Theta) be an indecomposable principally polarized abelian variety whose theta divisor can be written as a sum of a curve and a codimension two subvariety \\Theta=C+Y. 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