Seminar on Complex Analysis and Complex Geometry - Spring 2018

Wednesday, February 14, 2018, 3-4pm, PGH 646A

Title: Positive locally conformally Kaehler potentials

Speaker: Liviu Ornea, University of Bucharest

Abstract: Locally Conformally Kaehler (LCK) manifolds are complex manifolds covered by Kaehler ones, with deck group acting by holomorphic homotheties wrt the Kaehler form (in particular, this covering is never compact). Among the examples: all Hopf manifolds, Kodaira surfaces, some Inoue surfaces etc. An important subclass is formed by those LCK manifolds for which the Kaehler form on the covering has global potential. If such a global potential exists on a Kaehler covering, is acted on by homotheties by the deck group (i.e. it is automprphic), and is positive, the (compact) LCK manifold can be embedded into a Hopf manifold and, moreover, has a rather well understood topology. I shall show that, once an automorphic potential exists, one can construct a strictly positive one, too. This is joint work with Misha Verbitsky.