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