Bott-Chern hypercohomology and bimeromorphic invariants

Abstract The aim of this article is to study the geometry Bott-Chern hypercohomology from bimeromorphic point view. We construct some new invariants involving cohomology for sheaf germs pluriharmonic functions, truncated holomorphic de Rham cohomology, and cohomology. To define these invariants, by using a sheaf-theoretic approach, we establish blow-up formula together with canonical morphism hypercohomology. In particular, compute compact complex threefolds, such as Iwasawa manifolds quintic threefolds.