Degeneration of Kahler-Einstein hypersurfaces in complex torus to generalized pair of pants decomposition

Abstract

In this paper we show that the convergence of complete Kahler-Einstein hypersurfaces in complex torus in the sense of Cheeger-Gromov will canonically degenerate the underlying manifolds into "pair of pants" decomposition. We also construct minimal Lagrangian tori that represent the vanishing cycles of the degeneration.

Revised version. Some clarification made and an example added