On uniformization of compact Kähler manifolds with negative first chern class by bounded symmetric domains

We consider two complementary problems: given a compact Kähler manifold with negative first Chern Class, when is its universal cover a Bounded Symmetric Domain? And if it is, which Bounded Symmetric Domain is it? Existing literature is discussed, with particular attention given to two recent papers of Catanese and Di Scala ([CDS12] and [CDS]) which answer both questions first for Bounded Symmetric Domains of Tube Type, and then for all Bounded Symmetric Domains without Ball Factors. Using work of Yau and others on ball quotients we extend the main result of [CDS] to all bounded Symmetric Domains, including those with ball factors, thus answering the two questions posed in full generality.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2014

Author dc:creator

• Mckenzie, Daniel

Advisors dc:contributor.advisor

• Hughes, Kenneth
• Martin, Rob

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/9609

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/9609