Two formulas for the BR multiplicity
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Kleiman_Two formulas.pdf
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130.91 KB
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Author(s)
Kleiman, Steven L.
Date Issued
July 2016
Journal
ANNALI DELL'UNIVERSITA' DI FERRARA
Publisher
Springer-Verlag
Citation
Kleiman, Steven L. “Two Formulas for the BR Multiplicity.” ANNALI DELL’UNIVERSITA’ DI FERRARA (2016): n. pag.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s11565-016-0250-2
