  We revisit the construction of elliptic class given by Borisov and Libgober
for singular algebraic varieties. Assuming torus action we adjust the theory to
equivariant local situation. We study theta function identities having
geometric origin. In the case of quotient singularities $\mathbb C^n/G$, where
$G$ is a finite group the theta identities arise from McKay correspondence. The
symplectic singularities are of special interest. The Du Val surface
singularity $A_n$ leads to a remarkable formula.
