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arXiv · 1211.6032

The Index Theorem for Quasi-Tori

Tsz On Mario Chan
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Abstract

The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the signature of the associated hermitian form. In this article, 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 $L^2$-methods coupled with the Kazama-Dolbeault isomorphism and Bochner-Kodaira formulas.

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Tsz On Mario Chan. 2013-03-04. The Index Theorem for Quasi-Tori. https://doi.org/10.1016/j.matpur.2013.01.019

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