Through the looking glass.

*(English)*Zbl 0935.32020
Phong, Duong H. (ed.) et al., Mirror symmetry III. Proceedings of the conference on Complex geometry and mirror symmetry. MontrĂ©al, Canada, 1995. New York, NY, Cambridge, MA: AMS, International Press. AMS/IP Stud. Adv. Math. 10, 263-277 (1999).

Summary: It is frequently possible to produce new Calabi-Yau threefolds from old ones by a process of allowing the complex structure to degenerate to a singular one, and then performing a resolution of singularities. (Some care is needed to ensure that the Calabi-Yau condition be preserved.) There has been speculation that all Calabi-Yau threefolds could be linked in this way, and considerable evidence has been amassed in this direction. We propose here a natural way to relate this construction to the string-theoretic phenomenon known as “mirror symmetry”. We formulate a conjecture which in principle could predict mirror partners for all Calabi-Yau threefolds, provided that all were indeed linked by the degeneration/resolution process. The conjecture produces new mirrors from old, and so requires some initial mirror manifold construction – such as Greene-Plesser orbifolding – as a starting point.

For the entire collection see [Zbl 0908.00032].

For the entire collection see [Zbl 0908.00032].