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We are studying here the relation between the stability the fact that the bundle is verifying a condition $(R)$ introduced by Raynaud : we prove that $E_{L}$ is semi stable when $C$ is general. We also prove that $E_{L}$ is verifying $(R)$ when $\\deg(L) \\geq 2g$ or when $L$ is generic. Finally we prove that for each $p$ in $\\{2,..., \\mathrm{rg}(E_{L})-2\\}$, if $\\deg(L) \\geq 2g+2$ then $\\Lambda^{p}E_{L}$ "},"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":"math/0309277","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2003-09-17T13:41:02Z","cross_cats_sorted":[],"title_canon_sha256":"db366ebd9160eba7687d8569ea9e725c7d78e02088ba3cfe777a442b14932ee0","abstract_canon_sha256":"5bf70de6a1306b23b9ee8ee1ff7f6a29e199e8d51c14843795b91e902d5a4a3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:37:43.726440Z","signature_b64":"W10NCqAGvyvuQkqDfuR7QsLQ+ud3wpw2uH5GDPfTm4CowqccTgT7J+x6TtcEH7bYEpKuEWvP+ZLo8TtTUCQ0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4f868beec041c9db0676f39850842985441030548e3a32f0c265b018c3267a1","last_reissued_at":"2026-07-04T14:37:43.726016Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:37:43.726016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stabilit\\'e des fibr\\'es $\\Lambda^{p}E_{L}$ et condition de Raynaud","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Olivier Schneider","submitted_at":"2003-09-17T13:41:02Z","abstract_excerpt":"Let $C$ be a smooth curve of genus $g \\geq 2$ on $\\C$. Let $L$ be a line bundle on $C$ generated by its global sections and let $E_{L}$ be the dual of the kernel of the evaluation map $e_{L}$. We are studying here the relation between the stability the fact that the bundle is verifying a condition $(R)$ introduced by Raynaud : we prove that $E_{L}$ is semi stable when $C$ is general. We also prove that $E_{L}$ is verifying $(R)$ when $\\deg(L) \\geq 2g$ or when $L$ is generic. 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