| Mirror symmetry of Calabi-Yau varieties can be interpreted as a duality of Lagrangian torus fibrations. Using this approach I will describe the construction of lagrangian sections and spheres in the mirror of a toric Calabi-Yau. I will then illustrate a correspondence between sections and line bundles on the toric Calabi-Yau and between spheres and sheaves supported on the compact toric divisors. We expect that this correspondence will satisfy the properties of homological mirror symmetry. |