  We study the elliptic genera of two-dimensional orbifold CFTs, where the
orbifolding procedure introduces du Val surface singularities on the target
space. The N=4 character decompositions of the elliptic genus contributions
from the twisted sectors at the singularities obey a consistent scaling
property, and contain information about the arrangement of exceptional rational
curves in the resolution. We also discuss how these twisted sector elliptic
genera are related to twining genera and Hodge elliptic genera for sigma models
with K3 target space.
