Deformations of equivelar Stanley-Reisner abelian surfaces

Abstract

The versal deformation of Stanley-Reisner schemes associated to equivelar triangulations of the torus is studied. The deformation space is defined by binomials and there is a toric smoothing component which I describe in terms of cones and lattices. Connections to moduli of abelian surfaces are considered. The case of the M\"obius torus is especially nice and leads to a projective Calabi-Yau 3-fold with Euler number 6.