| I will apply results of Klaus Altmann and myself on deformations of Stanley Reisner schemes to the minimal triangulation of the torus. The smooth fibers are abelian surfaces and the resulting 10- dimensional versal deformation space has a surprisingly rich geometry and a mysterious connection to the Batyrev-Borisov study of complete intersections in toric varieties. In particular a Calabi Yau 3 fold with Euler number 6 appears. |