Two Formulas for the BR Multiplicity
arXiv:1507.08865
Abstract
We prove a projection formula, expressing a relative Buchsbaum--Rim multiplicity in terms of corresponding ones over a module-finite algebra of pure degree, generalizing an old formula for the ordinary (Samuel) multiplicity. Our proof is simple in spirit: after the multiplicities are expressed as sums of intersection numbers, the desired formula results from two projection formulas, one for cycles and another for Chern classes. Similarly, but without using any projection formula, we prove an expansion formula, generalizing the additivity formula for the ordinary multiplicity, a case of the associativity formula.
10 pages, to appear in the Annali dell'Università di Ferrara, in a special memorial volume honoring Bobi Lascu. This version has been revised following a referee's suggestions, but the technical mathematics is unchanged