广义$p-$ Kähler流形的真修改
Proper modifications of generalized $p-$Kähler manifolds
摘要：
本文考虑复流形之间的一个适当的修正$f : \tilde M \to M$，并研究了广义$p-$ Kähler性质何时从$M$回到$\tilde M$ .当$f$是在一点的爆破时，每个广义$p-$ Kähler性质都是守恒的，而当$f$是沿着子流形的爆破时，对于$p=1$也是如此。对于$p=n-1$，我们证明了紧致广义平衡流形类关于修改是封闭的，并且我们证明了基本形式可以在期望的上同调类中选择。在非紧情形下也得到了一些部分结果，最后给出了广义$p-$ Kähler流形的一些例子.
英文摘要：
In this paper, we consider a proper modification $f : \tilde M \to M$ between complex manifolds, and study when a generalized $p-$Kähler property goes back from $M$ to $\tilde M$. When $f$ is the blow-up at a point, every generalized $p-$Kähler property is conserved, while when $f$ is the blow-up along a submanifold, the same is true for $p=1$. For $p=n-1$, we prove that the class of compact generalized balanced manifolds is closed with respect to modifications, and we show that the fundamental forms can be chosen in the expected cohomology class. We get some partial results also in the non-compact case; finally, we end the paper with some examples of generalized $p-$Kähler manifolds.
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