Mirror Symmetry via 3-tori for a class of Calabi-Yau Threefolds

TL;DR

This paper demonstrates a concrete example of mirror symmetry for certain Calabi-Yau threefolds using the SYZ conjecture, focusing on dualizing special Lagrangian 3-tori to produce mirror pairs.

Contribution

It provides an explicit construction of mirror symmetry for Voisin-Borcea Calabi-Yau threefolds via dualizing special Lagrangian 3-tori, illustrating the SYZ approach.

Findings

Mirror symmetry for Voisin-Borcea threefolds is realized through dualizing special Lagrangian 3-tori.

The paper extends the SYZ conjecture to specific Calabi-Yau threefolds.

Explicit examples support the SYZ mirror construction in this context.

Abstract

We give an example of the recent proposed mirror construction of Strominger, Yau and Zaslow in ``Mirror Symmetry is T-duality,'' hep-th/9606040. The paper first considers mirror symmetry for K3 surfaces in light of this construction. We then consider the example of mirror symmetry for Calabi-Yau threefolds of the type considered by Voisin and Borcea, of the form SxE/involution where S is a K3 surface with involution, and E is an elliptic curve. We show how dualizing a family of special Lagrangian real 3-tori does actually produce the mirrors in these examples.