Compactifying torus fibrations over integral affine manifolds with singularities

Abstract

This is an announcement of the following construction: given an integral affine manifold $B$ with singularities, we build a topological space $X$ which is a torus fibration over $B$. The main new feature of the fibration $X\to B$ is that it has the discriminant in codimension 2.

13 pages, 4 figures, questions and suggestions are welcome!