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arXiv · 1008.2207

Generalized Borcea-Voisin Construction

Jimmy Dillies
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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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Jimmy Dillies. 2011-07-14. Generalized Borcea-Voisin Construction. https://doi.org/10.1007/s11005-011-0528-3

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