Riemann–Roch theorem
theorem that the Euler characteristic of the sheaf cohomology of a holomorphic line bundle on a Riemann surface equals the degree of the bundle plus half of the Euler characteristic of the surface
| rdfs:label |
"Riemann–Roch theorem"@en
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| schema:description |
"theorem that the Euler characteristic of the sheaf cohomology of a holomorphic line bundle on a Riemann surface equals the degree of the bundle plus half of the Euler characteristic of the surface"@en
|
|
schema:date |
"2026-09-12T10:52:39+00:00"^^xsd:dateTime |
| schema:version | 2544497391 |
| wikibase:identifiers | 4 |
| wikibase:sitelinks | 14 |
| wikibase:statements | 19 |
| p:P10376 | wd:statement/Q379048-4fad2531-42bb-8d02-5c7c-063aacf70d59 |
| p:P1318 | wd:statement/Q379048-bdb85016-48f4-1e99-bc79-8cd2653da769 |
| p:P138 | wd:statement/q379048-ae4a8765-4a9a-b271-d400-077b4c066c8a |
| wd:statement/q379048-f91631d3-4f5c-a664-76a1-3224dc8f3a30 | |
| p:P2384 | wd:statement/Q379048-c83e2ad9-4b3d-2a65-ccec-8a5c9f92e781 |
| p:P2534 | wd:statement/Q379048-5e8d7d7c-42e8-8e80-1987-d379cad4edfc |
| p:P2579 | wd:statement/Q379048-06C4C34C-6FD9-4121-BE30-CA0FBB526B84 |
| p:P31 | wd:statement/Q379048-CC39B77F-8B43-4B76-8149-4B999A0395C6 |
| p:P361 | wd:statement/Q379048-B491193D-3C86-4D47-BC3E-47B9C3E7F442 |
| p:P6104 | wd:statement/Q379048-557C3EFA-19F1-40D3-A979-5204E556CD3A |
| p:P6366 | wd:statement/Q379048-366DBBD7-28CA-48FB-AE01-0EA51546282E |
| p:P646 | wd:statement/Q379048-3713190B-A89B-48C6-80C7-33B019227B5B |
| p:P6781 | wd:statement/Q379048-04374532-49dd-6130-d954-692718244250 |
| p:P7235 | wd:statement/Q379048-3f4ba4f2-47af-de19-e6ae-55d96f39e317 |
| wd:statement/Q379048-66884d13-498c-0993-8c94-df93aa2a9adf | |
| wd:statement/Q379048-85f192fd-4084-d57c-f714-25d20d24f8c3 | |
| wd:statement/Q379048-92dd0d5b-4dbc-6383-0877-5fa76dd68362 | |
| wd:statement/Q379048-afc2ce3b-4c20-0035-9342-8868ccffc262 | |
| wd:statement/Q379048-f3a0439c-42f7-4a45-aec5-4920b1b999d0 | |
|
p:direct- |
<https:/ |
| wdt:P10376 | "mathematics/riemann-roch-theorem" |
| wdt:P1318 | Gustav Roch |
| wdt:P138 | Gustav Roch |
| Bernhard Riemann | |
| wdt:P2384 | compact Riemann surface |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>dim</mi><mo>⁡</mo><msup><mi data-mjx-texclass="OP" mathvariant="normal">H</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="normal">Σ</mi><mo>,</mo><mi>L</mi><mo stretchy="false">)</mo><mo stretchy="false">−</mo><mi>dim</mi><mo>⁡</mo><msup><mi data-mjx-texclass="OP" mathvariant="normal">H</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="normal">Σ</mi><mo>,</mo><mi>L</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>deg</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>L</mi><mo stretchy="false">)</mo><mo stretchy="false">+</mo><mn>1</mn><mo stretchy="false">−</mo><mi>g</mi><mo stretchy="false">(</mo><mi mathvariant="normal">Σ</mi><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2579 | algebraic geometry |
| wdt:P31 | theorem |
| wdt:P361 | list of theorems |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "2777639948" |
| wdt:P646 | "/m/01krvf" |
| wdt:P6781 | "Riemann-Roch_Theorem" |
| wdt:P7235 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi data-mjx-texclass="OP" mathvariant="normal">H</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi mathvariant="normal">Σ</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>L</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>deg</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>dim</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>g</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
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