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We construct a smooth family $\\mathcal{X}$ over $\\mathbb{C}$ with an embedding in $\\mathbb{C}\\mathbb{P}^{N} \\times \\mathbb{C}$ whose generic fiber is $X$ and the special fiber is the torus $(\\mathbb{C}^*)^n$ sitting in $\\mathbb{C}\\mathbb{P}^{N}$ via a monomial embedding. We use this to show that if $\\omega$ is an integral K\\\"ahler form on $X$ then for any $\\epsilon > 0$ there is an open subset $U_\\epsilon \\subset X$ such that $vol(X \\setminus U_\\epsilon) < \\epsilon$ and $U_\\epsilon$ is sympl"},"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":"1508.00316","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-08-03T05:33:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"745ec11f5f7ce070ab3285e3fd10d46b417ede3423f5089d10c221a4e98c2b0e","abstract_canon_sha256":"35b23eb18a1b326efc06352e29ebc065afe32dce0e2fa61c6ac48ad360be4c21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:50.536752Z","signature_b64":"DgblxuBOpGRPiVGXjYPNjbGUTPZj7WVJ6YucbzAuIx2N+hHmiPH/bcffNr5SFjNP571/7llyV7WS0wFwBlNECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a28a042eb86e571f4cb16b6e093c9ddee7658f13a874a4089ca64002488b9d2","last_reissued_at":"2026-05-18T00:04:50.536103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:50.536103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Toric degenerations and symplectic geometry of smooth projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.SG","authors_text":"Kiumars Kaveh","submitted_at":"2015-08-03T05:33:00Z","abstract_excerpt":"Let $X$ be an $n$-dimensional smooth complex projective variety embedded in $\\mathbb{C}\\mathbb{P}^{N}$. 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We use this to show that if $\\omega$ is an integral K\\\"ahler form on $X$ then for any $\\epsilon > 0$ there is an open subset $U_\\epsilon \\subset X$ such that $vol(X \\setminus U_\\epsilon) < \\epsilon$ and $U_\\epsilon$ is sympl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00316","kind":"arxiv","version":3},"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":"1508.00316","created_at":"2026-05-18T00:04:50.536176+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.00316v3","created_at":"2026-05-18T00:04:50.536176+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00316","created_at":"2026-05-18T00:04:50.536176+00:00"},{"alias_kind":"pith_short_12","alias_value":"RIUKAQXLQ3SX","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RIUKAQXLQ3SXD5GL","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RIUKAQXL","created_at":"2026-05-18T12:29:39.896362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RIUKAQXLQ3SXD5GLC23OBE6J3X","json":"https://pith.science/pith/RIUKAQXLQ3SXD5GLC23OBE6J3X.json","graph_json":"https://pith.science/api/pith-number/RIUKAQXLQ3SXD5GLC23OBE6J3X/graph.json","events_json":"https://pith.science/api/pith-number/RIUKAQXLQ3SXD5GLC23OBE6J3X/events.json","paper":"https://pith.science/paper/RIUKAQXL"},"agent_actions":{"view_html":"https://pith.science/pith/RIUKAQXLQ3SXD5GLC23OBE6J3X","download_json":"https://pith.science/pith/RIUKAQXLQ3SXD5GLC23OBE6J3X.json","view_paper":"https://pith.science/paper/RIUKAQXL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.00316&json=true","fetch_graph":"https://pith.science/api/pith-number/RIUKAQXLQ3SXD5GLC23OBE6J3X/graph.json","fetch_events":"https://pith.science/api/pith-number/RIUKAQXLQ3SXD5GLC23OBE6J3X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RIUKAQXLQ3SXD5GLC23OBE6J3X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RIUKAQXLQ3SXD5GLC23OBE6J3X/action/storage_attestation","attest_author":"https://pith.science/pith/RIUKAQXLQ3SXD5GLC23OBE6J3X/action/author_attestation","sign_citation":"https://pith.science/pith/RIUKAQXLQ3SXD5GLC23OBE6J3X/action/citation_signature","submit_replication":"https://pith.science/pith/RIUKAQXLQ3SXD5GLC23OBE6J3X/action/replication_record"}},"created_at":"2026-05-18T00:04:50.536176+00:00","updated_at":"2026-05-18T00:04:50.536176+00:00"}