TL;DR
This paper generalizes the Borcea-Voisin construction of Calabi-Yau threefolds and fourfolds to prime order automorphisms, classifies the resulting topological types, and investigates mirror symmetry and resolutions.
Contribution
It extends the original construction to any prime order, classifies topological types, and analyzes mirror symmetry and resolutions in higher dimensions.
Findings
In dimension 4, orbifolds with involution admit crepant resolutions and form mirror pairs.
For odd primes, minimal resolutions are generally absent, affecting mirror symmetry.
The construction broadens the landscape of Calabi-Yau orbifolds and their mirror relationships.
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.
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