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Dual cones and mirror symmetry for generalized Calabi-Yau manifolds. (English) Zbl 0927.14019
Greene, B. (ed.) et al., Mirror symmetry II. Cambridge, MA: International Press, AMS/IP Stud. Adv. Math. 1, 71-86 (1997).
An appropriate mathematical framework for explicit constructions of mirror pairs of Calabi-Yau manifolds is presented. One introduces a special class of convex rational polyhedral cones which allows the construction of generalized Calabi-Yau manifolds and a natural combinatorial duality satisfied by these cones is established. It is shown that the generalized method given in the paper includes as special cases all already known examples of mirror pairs proposed by physicists. In particular, the mirrors of rigid Calabi-Yau manifolds are constructed.
For the entire collection see [Zbl 0905.00079].
Reviewer: G.Zet (Iaşi)

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
83E30 String and superstring theories in gravitational theory
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