https://diffgeom.subwiki.org/w/index.php?action=history&feed=atom&title=Kodaira_vanishing_theoremKodaira vanishing theorem - Revision history2026-06-11T21:54:57ZRevision history for this page on the wikiMediaWiki 1.41.2https://diffgeom.subwiki.org/w/index.php?title=Kodaira_vanishing_theorem&diff=802&oldid=prevVipul: 1 revision2008-05-18T19:47:54Z<p>1 revision</p>
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==Statement==<br />
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Let <math>L</math> be a holomorphic line bundle on a compact [[Kahler manifold]] <math>M</math>, whose topological Chern class can be represented by a closed <math>(1,1)</math>-form which is positive definite. Let <math>E</math> be any other holomorphic vector bundle. Then the cohomology groups <math>H^q(M, E \otimes L)</math> vanish for large enough <math>r</math> whenever <math>q</math> is at least 1.<br />
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==Relation with other results==<br />
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===Kodaira embedding theorem===<br />
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{{further|[[Kodaira embedding theorem]]}}<br />
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===Lichnerowicz vanishing theorem===<br />
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{{further|[[Lichnerowicz vanishing theorem]]}}</div>Vipul