Finiteness of Complete Intersection Calabi Yau Threefolds

Abstract: Of many modern constructions in geometry Calabi Yau manifolds hold special relevance in theoretical physics. These manifolds naturally arise from the study of compactification of certain string theories. In particular Calabi Yau manifolds of dimension three, commonly known as threefolds, are widely used for compactifications of heterotic string theories. Among the many constructions, that of complete intersection Calabi Yau manifolds (CICY) is generally regarded to be the simplest. Furthermore, CICY threefolds have been proven to exist only in finite number. In the following text CICY manifolds will be analyzed, with particular attention to threefolds. A general description of some of their topological quantities and their calculation is offered. Lastly, a proof of the finiteness of CICY threefolds is given.