Geometric Aspects of Mirror Symmetry

Details Geometric Aspects of Mirror Symmetry Geometric Aspects of Mirror Symmetry

2000-07-14

arxiv.org/abs/math/0007090v1

Mathematics Unlimited -- 2001 and Beyond (B. Enquist and W. Schmid, eds.), Springer-Verlag, 2001, pp. 899-918

Mathematics

Algebraic Geometry

21 pages, 3 figures

Scientific paper

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.

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