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More precisely, let $(X,B)$ be a holomorphic family of sub log canonical, log-Calabi-Yau complex varieties parameterized by the punctured unit disk. Let $\\eta$ be a meromorphic volume form on $X$ with poles along $B$. We show that the (possibly infinite) measures induced by the restriction of the $\\eta$ to a fiber converge to a measure on the Berkovich analytification as we approach the puncture. The convergence take"},"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":"1911.07307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-11-17T17:46:21Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"7b824af65b4ceeea46374c2cd29dd5a48fdf9a622a3f4f0e45c279a82599bd56","abstract_canon_sha256":"2ec90c57cb1583da167cede0913510e2e96068dfd047f618213f94a12d16592e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:19:45.273122Z","signature_b64":"7K/Ll4XLEI+IlDRStPImO+dh49SoWUKObq/+g4lREjBJi8DWRPwcqOdzXtuZO2h3QL5AA5uATfG7Y84Jwzv5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81227fc0951e888ac446fd1c29b47f156edf8d606fe6d90972ad34d792b02c5c","last_reissued_at":"2026-07-05T00:19:45.272702Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:19:45.272702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of volume forms on a family of log-Calabi-Yau varieties to a non-Archimedean measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Sanal Shivaprasad","submitted_at":"2019-11-17T17:46:21Z","abstract_excerpt":"We study the convergence of volume forms on a degenerating holomorphic family of log-Calabi-Yau varieties to a non-Archimedean measure, extending a result of Boucksom and Jonsson. More precisely, let $(X,B)$ be a holomorphic family of sub log canonical, log-Calabi-Yau complex varieties parameterized by the punctured unit disk. Let $\\eta$ be a meromorphic volume form on $X$ with poles along $B$. We show that the (possibly infinite) measures induced by the restriction of the $\\eta$ to a fiber converge to a measure on the Berkovich analytification as we approach the puncture. 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