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These fit into a finite-type family, which is functorial in $X$, and which is topologically a family of $\\mathbb{C}$-weighted configuration spaces. We verify our construction agrees with an analogous construction in the Deligne category $Rep(S_{d})$ for $d \\in \\mathbb{C}$.\n  We next classify the singularity locus and branching behavio"},"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":"1903.05011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-03-12T15:53:51Z","cross_cats_sorted":[],"title_canon_sha256":"fb73f50adb8fc3f6a3bd0b7a39b301d092127721869028753d274260dead522a","abstract_canon_sha256":"a0c54e28b28feaf0d5ebd5f47983cdc5b058a27130c790d2ce632d6526dbb005"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:26.535637Z","signature_b64":"Q31JGEHncDhakgHbbLjXrevQq0KqfrsMVQgXmCjvUtpUB6ytMgNCN4rqcx4an5y2YST2xAiuer4yl8rX+WCgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9ada9b2a6c98f33b5054a2a421872cde02cfecaedd7f2ab5773cf89164368a7","last_reissued_at":"2026-05-17T23:51:26.535143Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:26.535143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Incidence strata of affine varieties with complex multiplicities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dennis Tseng, Hunter Spink","submitted_at":"2019-03-12T15:53:51Z","abstract_excerpt":"To each affine variety $X$ and $m_1,\\ldots,m_k\\in \\mathbb{C}$ such that no subset of the $m_i$ add to zero, we construct a variety which for $m_1,\\ldots,m_k \\in \\mathbb{N}$ specializes to the closed $(m_1,\\ldots,m_k)$-incidence stratum of $Sym^{m_1+\\ldots+m_k}X$. 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