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Let $V_L$ be the $\\mathfrak{S}_n$-vector bundle on $X^n$ defined as the exterior direct sum $L \\boxplus \\cdots \\boxplus L$. We prove that the Bridgeland-King-Reid transform $\\mathbf{\\Phi}(S^k L^{[n]})$ of symmetric powers $S^k L^{[n]}$ is quasi isomorphic to the last term of a finite decreasing filtration on the natural vector bundle $S^k V_L$, defined by kernels of operators $D^l_L$,"},"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":"1502.07595","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-26T15:35:01Z","cross_cats_sorted":[],"title_canon_sha256":"7cd4f905adf2c6534256b407ffd1f520537ba851b723e2e4394f7c6af2fa7fe9","abstract_canon_sha256":"ed084e5ec69dab201d1c4b5d2423392025a26e8aa878e115d6aaeff381016f8d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:50.792627Z","signature_b64":"A8r07dm54yVgcWACnthAnKgiY5oEX97qMPAjfyXTbJGuRm67/26+nCXJIR0L9ldJ6G96QWVw/xe/lw59NmNaBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c93148973035cb357802661f173dbc7294267e354a1b77824ac818d9ec8e0eb6","last_reissued_at":"2026-05-18T01:23:50.791960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:50.791960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher symmetric powers of tautological bundles on Hilbert schemes of points on a surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luca Scala","submitted_at":"2015-02-26T15:35:01Z","abstract_excerpt":"We study general symmetric powers $S^k L^{[n]}$ of a tautological bundle $L^{[n]}$ on the Hilbert scheme $X^{[n]}$ of $n$ points over a smooth quasi-projective surface $X$, associated to a line bundle $L$ on $X$. Let $V_L$ be the $\\mathfrak{S}_n$-vector bundle on $X^n$ defined as the exterior direct sum $L \\boxplus \\cdots \\boxplus L$. We prove that the Bridgeland-King-Reid transform $\\mathbf{\\Phi}(S^k L^{[n]})$ of symmetric powers $S^k L^{[n]}$ is quasi isomorphic to the last term of a finite decreasing filtration on the natural vector bundle $S^k V_L$, defined by kernels of operators $D^l_L$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07595","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.07595","created_at":"2026-05-18T01:23:50.792065+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.07595v2","created_at":"2026-05-18T01:23:50.792065+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07595","created_at":"2026-05-18T01:23:50.792065+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZEYURFZQGXFT","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZEYURFZQGXFTK6AC","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZEYURFZQ","created_at":"2026-05-18T12:29:52.810259+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2211.03901","citing_title":"On the cohomology of tautological bundles over Quot schemes of curves","ref_index":18,"is_internal_anchor":true},{"citing_arxiv_id":"2604.15098","citing_title":"Tangent bundle of punctual Hilbert scheme and distinguishing products of varieties","ref_index":25,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZEYURFZQGXFTK6ACMYPROPN4OK","json":"https://pith.science/pith/ZEYURFZQGXFTK6ACMYPROPN4OK.json","graph_json":"https://pith.science/api/pith-number/ZEYURFZQGXFTK6ACMYPROPN4OK/graph.json","events_json":"https://pith.science/api/pith-number/ZEYURFZQGXFTK6ACMYPROPN4OK/events.json","paper":"https://pith.science/paper/ZEYURFZQ"},"agent_actions":{"view_html":"https://pith.science/pith/ZEYURFZQGXFTK6ACMYPROPN4OK","download_json":"https://pith.science/pith/ZEYURFZQGXFTK6ACMYPROPN4OK.json","view_paper":"https://pith.science/paper/ZEYURFZQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.07595&json=true","fetch_graph":"https://pith.science/api/pith-number/ZEYURFZQGXFTK6ACMYPROPN4OK/graph.json","fetch_events":"https://pith.science/api/pith-number/ZEYURFZQGXFTK6ACMYPROPN4OK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZEYURFZQGXFTK6ACMYPROPN4OK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZEYURFZQGXFTK6ACMYPROPN4OK/action/storage_attestation","attest_author":"https://pith.science/pith/ZEYURFZQGXFTK6ACMYPROPN4OK/action/author_attestation","sign_citation":"https://pith.science/pith/ZEYURFZQGXFTK6ACMYPROPN4OK/action/citation_signature","submit_replication":"https://pith.science/pith/ZEYURFZQGXFTK6ACMYPROPN4OK/action/replication_record"}},"created_at":"2026-05-18T01:23:50.792065+00:00","updated_at":"2026-05-18T01:23:50.792065+00:00"}