A residue-theoretic representation is given for massless matter fields in (quotients of) (weighted) Calabi-Yau complete intersection models and the corresponding chiral operators in Landau-Ginzburg orbifolds. The well-known polynomial deformations are thus generalized, and the universal but somewhat abstract Koszul computations acquire a concrete realization and a general but more heuristic reinterpretation. Also, a direct correspondence with a BRST type analysis of constrained systems emerges naturally.
