DUAL POLYHEDRA, MIRROR SYMMETRY AND GINZBURG-LANDAU ORBIFOLDS
1996 ◽
Vol 11
(05)
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pp. 389-396
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Keyword(s):
The One
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New geometrical features of the Ginzburg-Landau orbifolds are presented, for models with a typical type of superpotential. We show the one-to-one correspondence between some of the (a, c) states with U(1) charges (−1, 1) and the integral points on the dual polyhedra, which are useful tools for the construction of mirror manifolds. Relying on toric geometry, these states are shown to correspond to the (1, 1) forms coming from blowing-up processes. In terms of the above identification, it can be checked that the monomial-divisor mirror map for Ginzburg-Landau orbifolds, proposed by the author, is equivalent to that mirror map for Calabi-Yau manifolds obtained by the mathematicians.