Calabi-Yau manifolds and their degenerations

Abstract

Calabi-Yau manifolds are geometric objects of central importance in several branches of mathematics, including differential geometry, algebraic geometry, and mathematical physics. In this paper, we give a brief introduction to the subject aimed at a general mathematical audience and present some of our results that shed some light on the possible ways in which families of Calabi-Yau manifolds can degenerate. © 2012 New York Academy of Sciences.