In the class of (0, 2) heterotic compactifications, which has been con
structed in the framework of gauged linear sigma models, the Calabi-Ya
u varieties X are realized as complete intersections of hypersurfaces
in toric varieties P-Sigma and the corresponding gauge bundles (or mor
e generally gauge sheaves) epsilon are defined by some short exact seq
uences. We show that there is yet another degree of freedom in reservi
ng singularities in such models which is related to the possible choic
es of nef partitions of the anticanonical divisors in Gorenstein-Fano
toric varieties P-Sigma. (C) 1998 Elsevier Science B.V.