On a mirror pair of Calabi-Yau
-folds, there is a one-to-one correspondence between the elements of the Hodge group and those of the
-dimensional cohomology group of its mirror space. In this paper, we show that there is an isomorphism between the group of the algebraic cycles and the group of the Lagrangian subvarieties of the mirror spaces. This correspondence provides a geometric realization of mirror symmetry at the level of subvarieties.
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