About: Ddbar lemma

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In complex geometry, the lemma (pronounced ddbar lemma) is a mathematical lemma about the de Rham cohomology class of a complex differential form. The -lemma is a result of Hodge theory and the Kähler identities on a compact Kähler manifold. Sometimes it is also known as the -lemma, due to the use of a related operator , with the relation between the two operators being and so .

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  • In complex geometry, the lemma (pronounced ddbar lemma) is a mathematical lemma about the de Rham cohomology class of a complex differential form. The -lemma is a result of Hodge theory and the Kähler identities on a compact Kähler manifold. Sometimes it is also known as the -lemma, due to the use of a related operator , with the relation between the two operators being and so . (en)
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  • Let be a complex manifold and be a differential form of bidegree for . Then is -closed if and only if for every point there exists an open neighbourhood containing and a differential form such that on . (en)
  • Let be a -closed -form on a compact Kähler manifold . Then the following are equivalent: (en)
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  • Lemma (en)
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  • In complex geometry, the lemma (pronounced ddbar lemma) is a mathematical lemma about the de Rham cohomology class of a complex differential form. The -lemma is a result of Hodge theory and the Kähler identities on a compact Kähler manifold. Sometimes it is also known as the -lemma, due to the use of a related operator , with the relation between the two operators being and so . (en)
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  • Ddbar lemma (en)
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