  In the class of (0,2) heterotic compactifications which has been constructed
in the framework of gauged linear sigma models the Calabi-Yau varieties X are
realized as complete intersections of hypersurfaces in toric varieties IP and
the corresponding gauge bundles (or more generally gauge sheaves) E are defined
by some short exact sequences. We show that there is yet another degree of
freedom in resolving singularities in such models which is related to the
possible choices of nef partitions of the anticanonical divisors in Gorenstein
Fano toric varieties IP.
