Making enumerative predictions by means of mirror symmetry

Details Making enumerative predictions by means of mirror symmetry Making enumerative predictions by means of mirror symmetry

1995-04-24

arxiv.org/abs/alg-geom/9504013v1

Mirror Symmetry II (B. Greene and S.-T. Yau, eds.), International Press, Cambridge, 1997, pp. 457-482

Physics

High Energy Physics

High Energy Physics - Theory

24 pages with 2 figures

Scientific paper

Given two Calabi--Yau threefolds which are believed to constitute a mirror pair, there are very precise predictions about the enumerative geometry of rational curves on one of the manifolds which can be made by performing calculations on the other. We review the mechanics of making these predictions, including a discussion of two conjectures which specify how the elusive ``constants of integration'' in the mirror map should be fixed. Such predictions can be useful for checking whether or not various conjectural constructions of mirror manifolds are producing reasonable answers.

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