|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Peer-reviewed Journal Articles, etc >
Localization of Bott-Chern classes and Hermitian residues
| Title: | Localization of Bott-Chern classes and Hermitian residues |
| Authors: | Correa, Mauricio, Jr. Browse this author | | Suwa, Tatsuo Browse this author →KAKEN DB |
| Keywords: | 32A27 | | 32C35 | | 32S65 | | 53C56 (primary) | | 14C30 | | 53B35 | | 53C05 | | 57R20 (secondary) |
| Issue Date: | Feb-2020 |
| Publisher: | John Wiley & Sons |
| Journal Title: | Journal of the London Mathematical Society. Second series |
| Volume: | 101 |
| Issue: | 1 |
| Start Page: | 349 |
| End Page: | 372 |
| Publisher DOI: | 10.1112/jlms.12273 |
| Abstract: | 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. |
| Rights: | 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. |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/76861 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
|
Submitter: 諏訪 立雄
|
