Algebraic Geometry Seminar

On generalized Inoue manifolds

Speaker: Andrei Pajitnov

Location: Warren Weaver Hall 317

Date: Tuesday, March 26, 2019, 3:30 p.m.


This talk is about a generalization of famous Inoue's surfaces.
Let M be a matrix in SL(2n+1,Z) having only one real eigenvalue which is simple.
 We associate to M a complex manifold T(M) of complex dimension n+1.
This manifold fibers over a circle with the fiber diffomorphic to
(2n+1)-dimensional torus and monodromy equal to the
transposed matrix M.  Our construction is elementary and does not use
algebraic number theory. We show that some of the Oeljeklaus-Toma
manifolds are biholomorphic to the manifolds of type T(M). We prove
that if M is not diagonalizable, then T(M)
does not admit a Kaehler structure and is not
homeomorphic to any of Oeljeklaus-Toma manifolds.
This is a joint work with Hisaaki Endo.