Calabi-Yau manifolds constructed by Borcea-Voisin method
Mitsuko Abe, Masamichi Sato
TL;DR
This paper constructs Calabi-Yau manifolds and their mirrors using the Borcea-Voisin method from K3 surfaces, analyzing their properties and mirror symmetry, with potential implications for S-duality in Seiberg-Witten theory.
Contribution
It applies the Borcea-Voisin construction to Calabi-Yau manifolds and explores mirror symmetry and properties in higher dimensions.
Findings
Confirmed mirror symmetry for Calabi-Yau 4-folds
Analyzed toric properties of the constructed manifolds
Potential applications to S-duality in Seiberg-Witten theory
Abstract
We construct Calabi-Yau manifolds and their mirrors from K3 surfaces. This method was first developed by Borcea and Voisin. We examined their properties torically and checked mirror symmetry for Calabi-Yau 4-fold case. From Borcea-Voisin 3-fold or 4-fold examples, it may be possible to probe the S-duality of Seiberg -Witten.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Advanced Algebra and Geometry