2000/07/14 by David R. Morrison
Mathematics · Physics and Astronomy · #math.AG #hep-th
published as Mathematics Unlimited -- 2001 and Beyond (B. Enquist and W. Schmid, eds.), Springer-Verlag, 2001, pp. 899-918 · 21 pages, 3 figures
arxiv created 2000/07/14 · arxiv updated 2009/11/30
The geometric aspects of mirror symmetry are reviewed, with an eye towards future developments. Given a mirror pair (X,Y) of Calabi-Yau threefolds, the best-understood mirror statements relate certain small corners of the moduli spaces of X and of Y. We will indicate how one might go beyond such statements, and relate the moduli spaces more globally. In fact, in the boldest version of mirror symmetry (the Strominger-Yau-Zaslow conjecture), the Calabi-Yau threefolds X and Y should be directly related to each other through a very geometric construction.