  We discuss an algebro-geometric description of Witten's phases of N=2
theories and propose a definition of their elliptic genus provided some
conditions on singularities of the phases are met. For Landau-Ginzburg phase
one recovers elliptic genus of LG models proposed in physics literature in
early 90s. For certain transitions between phases we derive invariance of
elliptic genus from an equivariant form of McKay correspondence for elliptic
genus. As special cases one obtains Landau-Giznburg/Calabi-Yau correspondence
for elliptic genus of weighted homogeneous potentials as well as certain
hybrid/CY correspondences.
