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- W3000610431 abstract "We study the stability of compact pseudo-Kahler 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 Kahler and any sufficiently small deformation of $X$ admits a Kahler metric by a well-known result of Kodaira and Spencer. We prove that compact pseudo-Kahler surfaces are also stable, but we show that stability fails in every complex dimension $ngeq 3$. Similar results are obtained for compact neutral Kahler 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-Kahler metric." @default.
- W3000610431 created "2020-01-23" @default.
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- W3000610431 date "2020-01-14" @default.
- W3000610431 modified "2023-09-27" @default.
- W3000610431 title "On the stability of compact pseudo-Kahler and neutral Calabi-Yau manifolds" @default.
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