Abstract:

We prove a blow-up formula for Dolbeault cohomologies of compact complex manifolds. As corollaries, we present a uniform proof for bimeromorphic invariance of (*,0)- and (0,*)- Hodge numbers on a compact complex manifold and also the differences of the same-type Bott-Chern and Hodge numbers on a complex threefold, 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 Frolicher spectral sequences at E1 on compact complex threefolds and fourfolds. This talk is based on the joint work arXiv: 1712.06749v1 with Song Yang and Xiangdong Yang.