{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:c2119140-62f5-42ca-b162-fd313d43319e", "labels": { "zh-CN": "复射影直线", "en": "complex projective line" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "47b98e84b03f9794f63839cbfade9c430e8b1a3c5f9b4677578fd4ff3b5d3132", "occurrences": [ { "concept_id": "urn:uuid:c2119140-62f5-42ca-b162-fd313d43319e", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/04-complex-projective-space", "anchor": "first-de54afbc6b9c88ca980a-zh", "chapter": "7", "section": "7.4", "offset": 4834, "range": [ 12914, 13231 ], "source_revision": "dece3546a425ea2c52b709472898bb8128e5d5d751614a636ab79e1e1bbfe61c", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "复射影直线(complex projective line)", "context": { "range": [ 12901, 13386 ], "quote": "我们要研究的是复数情形的[复射影直线(complex projective line)](../../../../../concepts/topology/complex-projective-space.md) $\\mathbf{C}P^1$。它较难直观呈现：从实空间的角度看，它是四维实空间中过原点的二维实平面所成的空间。在 $\\mathbf{C}P^1$ 上选取坐标的一种标准方式，是把向量", "quote_sha256": "95bc0dbfd1821d73c54bfae54c1abcab5a12f4d17a0a6fd315bbfd995763904a", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-07/04-complex-projective-space", "lang": "en", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-479bb0aa8420a92be043775f" }, { "concept_id": "urn:uuid:c2119140-62f5-42ca-b162-fd313d43319e", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "en", "route": "books/woit-qtgr/2025-10-20/en/chapter-07/04-complex-projective-space", "anchor": "first-de54afbc6b9c88ca980a-en", "chapter": "7", "section": "7.4", "offset": 5525, "range": [ 12938, 13248 ], "source_revision": "56ee7f1727deaa19e151a716a8ad06b4eb7d62437a0e4e97e582b9d242bc09a3", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "complex projective line", "context": { "range": [ 12909, 13530 ], "quote": "The complex analogue is the [complex projective line](../../../../../concepts/topology/complex-projective-space.md) $\\mathbf{C}P^1$. It is harder to visualize: as a real space, it consists of two-dimensional planes through the origin in four-dimensional space. One standard coordinate chart on $\\mathbf{C}P^1$ associates to the vector", "quote_sha256": "b6208f5ada1b85a012432c0d4c96685e4263a163f1d424bdb1164ff69ad1d039", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/04-complex-projective-space", "lang": "zh-CN", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-63087f30774763c95d72abfe" }, { "concept_id": "urn:uuid:c2119140-62f5-42ca-b162-fd313d43319e", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/04-complex-projective-space", "anchor": "first-d59757d7da819e92dd76-zh", "chapter": "7", "section": "7.4", "offset": 6684, "range": [ 14764, 15046 ], "source_revision": "dece3546a425ea2c52b709472898bb8128e5d5d751614a636ab79e1e1bbfe61c", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "复射影直线(complex projective line)", "context": { "range": [ 14674, 15125 ], "quote": "![](images/b5342b0cf696bb749d999e20cd9689e38a78211f64b725f7e75a22a52179020b.jpg) \n图 7.2：[复射影直线(complex projective line)](../../../../../concepts/topology/complex-projective-space.md) $\\mathbf{C}P^1$", "quote_sha256": "5cdc7f0033db09f008ccf2629d0e3def6ade71be3151556350f3d2b06743db6e", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-07/04-complex-projective-space", "lang": "en", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-b96c5d535de7220959b096f3" }, { "concept_id": "urn:uuid:c2119140-62f5-42ca-b162-fd313d43319e", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "en", "route": "books/woit-qtgr/2025-10-20/en/chapter-07/04-complex-projective-space", "anchor": "first-d59757d7da819e92dd76-en", "chapter": "7", "section": "7.4", "offset": 8090, "range": [ 15503, 15778 ], "source_revision": "56ee7f1727deaa19e151a716a8ad06b4eb7d62437a0e4e97e582b9d242bc09a3", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "complex projective line", "context": { "range": [ 15403, 15857 ], "quote": "![](images/b5342b0cf696bb749d999e20cd9689e38a78211f64b725f7e75a22a52179020b.jpg) \nFigure 7.2: The [complex projective line](../../../../../concepts/topology/complex-projective-space.md) $\\mathbf{C}P^1$", "quote_sha256": "900821bf29a4ce745f41c660f7c73f75a0c4d32c20594cd2312f0d4e6165cbea", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/04-complex-projective-space", "lang": "zh-CN", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-dcba423e72cb574d4819f806" } ], "registered_positions": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-07/04-complex-projective-space", "lang": "en", "section": "7.4", "signal": "term-mark", "label": "complex projective line", "english": "complex projective line", "offset": 3790 }, { "route": "books/woit-qtgr/2025-10-20/en/chapter-07/04-complex-projective-space", "lang": "en", "section": "7.4", "signal": "term-mark", "label": "complex projective line", "english": "complex projective line", "offset": 5782 }, { "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/04-complex-projective-space", "lang": "zh-CN", "section": "7.4", "signal": "term-mark", "label": "复射影直线", "english": "complex projective line", "offset": 3134 }, { "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/04-complex-projective-space", "lang": "zh-CN", "section": "7.4", "signal": "term-mark", "label": "复射影直线", "english": "complex projective line", "offset": 4411 } ], "statements": [], "resolved_references": [], "reading_order": [ "occ-479bb0aa8420a92be043775f", "occ-63087f30774763c95d72abfe", "occ-b96c5d535de7220959b096f3", "occ-dcba423e72cb574d4819f806" ], "recorded_dependencies": [], "reading_paths": [], "coverage": { "registered_positions": 4, "located_occurrences": 4, "whole_book_search_complete": false, "registered_positions_truncated": false, "independent_human_review_implied": false }, "unresolved": [], "base_revision": "f0a05bc872e0062f1f91b18113faef7654f11f7d753d90c25a44eb29700eeea5", "optional_enrichments": [] }