A primitive multiple scheme is a Cohen–Macaulay Y such that the associated reduced $$X=Y_{\mathrm{red}}$$ smooth, irreducible, and can be locally embedded in smooth variety of dimension $$\dim (X)+1$$ . If n multiplicity Y, there canonical filtration $$X=X_1\subset X_2\subset \cdots \subset X_n=Y$$ , $$X_i$$ i. The simplest example trivial to line bundle L on X: it nth infinitesimal neighborhoo...