Calabi-Yau Orbifolds and Torus Coverings

Understand

The theory of coverings of the two-dimensional torus is a standard part of algebraic topology and has applications in several topics in string theory, for example, in topological strings.

• This paper initiates applications of this theory to the counting of orbifolds of toric Calabi-Yau singularities, with particular attention to Abelian orbifolds of C^D.
• By doing so, the work introduces a novel analytical method for counting Abelian orbifolds, verifying previous algorithm results.
• One identifies a p-fold cover of the torus T^{D-1} with an Abelian orbifold of the form C^D/Z_p, for any dimension D and a prime number p.