Bott-Chern characteristic classes of blow-ups

TL;DR

This paper establishes a blow-up formula for Bott-Chern characteristic classes on compact complex manifolds, including a Riemann-Roch type result, and examines their behavior under blow-ups, exemplified by the Iwasawa manifold.

Contribution

It introduces a blow-up formula for Bott-Chern classes and a Riemann-Roch without denominators, advancing understanding of characteristic classes in complex geometry.

Findings

Proved a blow-up formula for Bott-Chern characteristic classes.

Established a Riemann-Roch type theorem without denominators.

Analyzed the behavior of Bott-Chern classes on the Iwasawa manifold after blow-up.

Abstract

We prove a blow-up formula for Bott-Chern characteristic classes of compact complex manifolds. To this end, we establish a version of Riemann-Roch without denominators for the Bott-Chern characteristic classes. In particular, as an application, we study the behaviour of the Bott-Chern characteristic classes of the Iwasawa manifold under a blow-up transformation.