2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/192205It is argued that every Calabi-Yau manifold $X$ with a mirror $Y$ admits a family of supersymmetric toroidal 3-cycles. Moreover the moduli space of such cycles together with their flat connections is precisely the space $Y$. The mirror transformation is equivalent to T-duality on the 3-cycles. The geometry of moduli space is addressed in a general framework. Several examples are discussed.20 pages, harvmac -- some references added, typos correctedHigh Energy Physics - TheoryAlgebraic Geometrytext