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Descripción
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| We study the stability of compact pseudo-Kähler manifolds, i.e. compact complex manifolds X endowed with a symplectic form compatible with the complex structure of X. When the corresponding metric is positive-definite, X is Kähler and any sufficiently small deformation of X admits a Kähler metric by a well-known result of Kodaira and Spencer. We prove that compact pseudo-Kähler surfaces are also stable, but we show that stability fails in every complex dimension n?3. Similar results are obtained for compact neutral Kähler and neutral Calabi-Yau manifolds. Finally, motivated by a question of Streets and Tian in the positive-definite case, we construct compact complex manifolds with pseudo-Hermitian-symplectic structures that do not admit any pseudo-Kähler metric. | |
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Internacional
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No |
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Nombre congreso
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Congreso bienal de la Real Sociedad Matemática Española |
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Tipo de participación
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960 |
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Lugar del congreso
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Santander |
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Revisores
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Si |
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ISBN o ISSN
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0000000000000 |
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DOI
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Fecha inicio congreso
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04/02/2019 |
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Fecha fin congreso
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08/02/2019 |
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Desde la página
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0 |
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Hasta la página
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0 |
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Título de las actas
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Congreso bienal de la Real Sociedad Matemática Española |