open access

https://hdl.handle.net/2115/76861

Localization of Bott-Chern classes and Hermitian residues

英語

57R20 (secondary)

2020-02

John Wiley & Sons

Journal of the London Mathematical Society. Second series

101(1)

349-372

We develop a theory of Cech-Bott-Chern cohomology and in this context we naturally come up with the relative Bott-Chern cohomology. In fact, Bott-Chern cohomology has two relatives and they all arise from a single complex. Thus, we study these three cohomologies in a unified way and obtain a long exact sequence involving the three. We then study the localization problem of characteristic classes in the relative Bott-Chern cohomology. For this, we define the cup product and integration in our framework and we discuss local and global duality morphisms. After reviewing some materials on connections, we give a vanishing theorem relevant to our localization. With these, we prove a residue theorem for vector bundles admitting a Hermitian connection compatible with an action of the non-singular part of a singular distribution. As a typical case, we discuss the action of a distribution on the normal bundle of an invariant submanifold (the so-called Camacho-Sad action) and give a specific example.

学術雑誌論文

Accepted Manuscript

This is the accepted version of the following article: Localization of Bott‐Chern classes and Hermitian residues, which has been published in final form at https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.12273.

0024-6107