Holomorphic line bundles on locally homogeneous complex manifolds (Geometry Day)
Time:15:30 - 16:30 Uhr
Abstract: The recent work of Guichard-Wienhard and Kapovich-Leeb-Porti has produced myriad new examples of locally homogeneous manifolds arising from quotients of domains of proper discontinuity via Anosov representations. In this talk, I will explain some of the complex geometry of the quotient manifolds that arise in this fashion. In particular, these manifolds arise as quotients of domains in flag varieties, where a rich theory of holomorphic line bundles exists due to the Borel-Bott-Weil theorem. Using this information, I will explain how to compute the Picard group of these quotient manifolds, and furthermore how to calculate some of the associated sheaf cohomology groups. Time permitting, I will discuss some interesting potential applications to invariant theory. This is joint work with David Dumas.