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For $g > (2r+2)(2r+1)$, we show how the bundle $E$ can be recovered from the tangent cone to the theta divisor $\\Theta_E$ at ${\\mathcal O}_C$. We use this to give a constructive proof and a sharpening of Brivio and Verra's theorem that the theta map $SU_C (r) -rightarrow |r \\Theta|$ is generically injective for large values of $g$."},"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":"1610.03456","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-10-11T18:37:11Z","cross_cats_sorted":[],"title_canon_sha256":"512c0ac904c186a794704d26a785c5cd5749a4458e0242774e43d0dcb136f924","abstract_canon_sha256":"a56fd6d55d508254b6208cf5a03ac5e48ba7193a021d97e9d3547037cbc66545"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:12.976382Z","signature_b64":"6VdCgmGlPS3TPs5O/Yf5CKFTWxdtKvnnR+Dw08Ob4QbKYsPGVhHUjTJlF1qDN382lrz/8KCEWvY0gZcMh6KpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f74ca5f05995d9750c16b0bd04be7f56a11d9119828a7600d0b506b8df6c5d2","last_reissued_at":"2026-05-17T23:53:12.975769Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:12.975769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tangent cones to generalised theta divisors and generic injectivity of the theta map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"George H. 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