# Algebraic Geometry Seminar

#### On generalized Inoue manifolds

**Speaker:**
Andrei Pajitnov

**Location:**
Warren Weaver Hall 317

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

**Synopsis:**

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.