Dolbeault cohomologies of blowing up complex manifolds
Dolbeault cohomologies of blowing up complex manifolds
复制标题
炸毁复流形的 Dolbeault 上同调
DOI：
10.1016/j.matpur.2019.01.016
复制
发表时间：
2019
影响因子：
2.3
通讯作者：
Yang Xiangdong
中科院分区：
文献类型：
--
作者：
Rao Sheng;Yang Song;Yang Xiangdong
通过引入相对Dolbeault上同调，证明了紧致复流形的Dolbeault上同调的爆破公式。作为推论，我们给出了紧致复流形上(·，0)-和(0，·)-Hodge数的双纯不变性的一致证明，并得到了具有相等(1，1)-Hodge数或等价的第二Betti数的紧致复流形上的双纯映射的弱因式分解的爆破次数和爆破次数相等.列举了后一种情况的许多例子。受此启发，我们得到了紧复数三重和四重的Frölicher谱序列退化的双纯稳定性。
We prove a blow-up formula for Dolbeault cohomologies of compact complex manifolds by introducing relative Dolbeault cohomology. As corollaries, we present a uniform proof for bimeromorphic invariance of (•, 0)-and (0, •)-Hodge numbers on a compact complex manifold, and obtain the equality for the numbers of the blow-ups and blow-downs in the weak factorization of the bimeromorphic map between two compact complex manifolds with equal (1, 1)-Hodge number or equivalently second Betti number. Many examples of the latter one are listed. Inspired by these, we obtain the bimeromorphic stability for degeneracy of the Frölicher spectral sequences at E1on compact complex threefolds and fourfolds.