In this note we survey and discuss the main results on the multiplicity sequence we introduced in former papers as a generalization of Samuel's multiplicity. We relate this new multiplicity to other numbers introduced in different contests, for example the Segre numbers of Gaffney and Gassler and the Hilbert coefficients defined by Ciupercă. Discussing some examples we underline the usefulness of the multiplicity sequence for concrete calculations in algebraic geometry using computer algebra systems.
R. Achilles, M. Manaresi (2006). Generalized Samuel Multiplicities and Applications. RENDICONTI DEL SEMINARIO MATEMATICO, 64 (4), 345-372.
Generalized Samuel Multiplicities and Applications
ACHILLES, HANS JOACHIM RUDIGER;MANARESI, MIRELLA
2006
Abstract
In this note we survey and discuss the main results on the multiplicity sequence we introduced in former papers as a generalization of Samuel's multiplicity. We relate this new multiplicity to other numbers introduced in different contests, for example the Segre numbers of Gaffney and Gassler and the Hilbert coefficients defined by Ciupercă. Discussing some examples we underline the usefulness of the multiplicity sequence for concrete calculations in algebraic geometry using computer algebra systems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
