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Letting $\\fp$ denote the $R$-submodule generated by the (image of the) syzygy module of $\\Omega_{A/k}$ and $\\fz$ the syzygy module of $\\mathcal{D}$, there is"},"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":"1112.4427","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-19T18:22:39Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"46ce0f73d12104e3e826e3a4e32e9c782e5c3270ab70be98afcdf50ebad6b882","abstract_canon_sha256":"e247d27839fffbd28d16b49f1d8918a70de07d9751d0bb2b6f428f9bc76f6e65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:36.816965Z","signature_b64":"79uDIv42TGIenue+TWyo+yqUcBjLxNYrfUV2tQsjDDWAkLWsOKdWBJWSFW+Mn4d3MJGkaTtDUv+JxFCDRaUfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f247ec48a82205311e7c5759a007cf39c5578c0ebe9aaabe58f89fb50ae8f4cc","last_reissued_at":"2026-05-18T01:12:36.816562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:36.816562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Syzygies of differentials of forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Aron Simis (Universidade Federal de Pernambuco, Brazil), Isabel Bermejo (Universidad de La Laguna, Philippe Gimenez (Universidad de Valladolid, Spain)","submitted_at":"2011-12-19T18:22:39Z","abstract_excerpt":"Given a standard graded polynomial ring $R=k[x_1,...,x_n]$ over a field $k$ of characteristic zero and a graded $k$-subalgebra $A=k[f_1,...,f_m]\\subset R$, one relates the module $\\Omega_{A/k}$ of K\\\"ahler $k$-differentials of $A$ to the transposed Jacobian module $\\mathcal{D}\\subset \\sum_{i=1}^n R dx_i$ of the forms $f_1,...,f_m$ by means of a {\\em Leibniz map} $\\Omega_{A/k}\\rar \\mathcal{D}$ whose kernel is the torsion of $\\Omega_{A/k}$. 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