Arkiv för Matematik

Volume 61 (2023)

Number 1

Intersection theory and Chern classes in Bott–Chern cohomology

Pages: 211 – 265

DOI: https://dx.doi.org/10.4310/ARKIV.2023.v61.n1.a11

Author

Xiaojun Wu (Mathematics VIII, Universität Bayreuth, Germany)

Abstract

In this article, we study the axiomatic approach of Grivaux in [Gri10] for rational Bott–Chern cohomology, and use it in particular to define Chern classes of coherent sheaves in rational Bott–Chern cohomology. This method also allows us to derive a Riemann–Roch–Grothendieck formula for a projective morphism between smooth complex compact manifolds.

Full Text (PDF format)

Received 16 June 2021

Received revised 29 September 2022

Accepted 10 October 2022

Published 26 April 2023