论文标题
关于紧凑的伪-Kähler和中性的calabi-yau歧管的稳定性
On the stability of compact pseudo-Kähler and neutral Calabi-Yau manifolds
论文作者
论文摘要
我们研究紧凑型伪kähler歧管的稳定性，即紧凑型复杂歧管$ x $，具有与$ x $的复杂结构兼容的符合形式。当相应的度量为正定标准时，$ x $是kähler，任何足够小的$ x $变形都可以通过Koudaira和Spencer的众所周知的结果来承认Kähler指标。我们证明，紧凑的伪-Kähler表面也稳定，但我们表明稳定性在每个复杂维度$ n \ geq 3 $中都失败。紧凑的中性kähler和中性的calabi-yau歧管获得了类似的结果。最后，在正常情况下，以街道和田的问题为动机，我们用不承认任何伪-Kähler指标的伪-------响应结构来构建紧凑的复杂歧管。
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 $n\geq 3$. 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.
