Document Type

Article

Publication Date

4-1-2012

Publication Title

Letters in Mathematical Physics

DOI

10.1007/s11005-011-0528-3

ISSN

1573-0530

Abstract

C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution. In this paper, we generalize the construction of Borcea and Voisin to any prime order and build three and four dimensional Calabi-Yau orbifolds. We classify the topological types that are obtained and show that, in dimension 4, orbifolds built with an involution admit a crepant resolution and come in topological mirror pairs. We show that for odd primes, there are generically no minimal resolutions and the mirror pairing is lost.

Comments

This version of the paper was obtained from arXIV.org. In order for the work to be deposited in arXIV.org, it must be available under the Creative Commons Attribution license, Creative Commons Attribution-Noncommercial-ShareAlike license, or Create Commons Public Domain Declaration. The publisher's final edited version of this article is available at Letters in Mathematical Physics.

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