Bott-Chern hypercohomology and bimeromorphic invariants

TL;DR

This paper investigates the geometry of Bott-Chern hypercohomology, introducing new bimeromorphic invariants and establishing formulas to compute these invariants for complex threefolds, enhancing understanding of complex manifold classification.

Contribution

It constructs new bimeromorphic invariants related to Bott-Chern hypercohomology and establishes a blow-up formula using a sheaf-theoretic approach.

Findings

Computed invariants for Iwasawa manifolds

Computed invariants for quintic threefolds

Established a blow-up formula for Bott-Chern hypercohomology

Abstract

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.