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We give a complete characterization of which such matrices have the property that a general form of degree $d$ in $\\mathbb C[x_0,x_1,x_2]$ can be written as the determinant of a matrix of forms $(f_{ij})$ with $\\deg f_{ij} = m_{ij}$ (of course $f_{ij} = 0$ if $m_{ij} < 0$). As a consequence, we answer the related question of wh"},"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":"1012.3396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-15T17:34:53Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"b1580461441eb2a3fc01e81794abc762cde609696e8cc1c573705e32498b2dbb","abstract_canon_sha256":"87acd2634bc6362915845e37e1d0eb11c8975fa657d233a28093cd44a3ae3aa2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:16.944346Z","signature_b64":"jp1ttqzpkYT32L/xX22mbQXATQl57DekMFgiNiot3AgfuB8jp+uLOv3NpSv/opdLNCPAx+F/oJs/uevcEYN4Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3048f73fe31800082c1e117d9aaccf982bd606802b3f2a7d110071127ebc4f15","last_reissued_at":"2026-05-18T04:33:16.943750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:16.943750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Determinantal representation and subschemes of general plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Juan Migliore, Luca Chiantini","submitted_at":"2010-12-15T17:34:53Z","abstract_excerpt":"Let $M = (m_{ij})$ be an $n \\times n$ square matrix of integers. 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