THE INDEX THEOREM FOR QUASI-TORI

The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the numbers of negative and positive eigenvalues of the associated hermitian form. In this thesis, this theorem is generalized to quasi-tori, i.e. connected complex abelian Lie groups which are not necessarily compact. In view of the Remmert–Morimoto decomposition of quasi-tori as well as the Künneth formula, it suffices to consider only Cousin-quasi-tori, i.e. quasi-tori which have no non-constant holomorphic functions. The Index theorem is generalized to holomorphic line bundles, both linearizable and non-linearizable, on Cousin-quasi-tori using L2-methods coupled with the Kazama–Dolbeault isomorphism and Bochner–Kodaira formulas.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Bayreuth

Year

2012

Author dc:creator

• Chan, Tsz On Mario

Contributors dc:contributor

• Catanese, Fabrizio

Repository record source_url

https://epub.uni-bayreuth.de/id/eprint/157/

OAI identifier oai:identifier

oai:epub.uni-bayreuth.de:157