Let I be a homogeneous ideal in a polynomial ring P over a field. By Macaulay’s Theorem there exists a lexicographic ideal L = Lex(I) with the same Hilbert function of I. Irena Peeva has proved that the Betti numbers of P/I can be obtained from the graded Betti numbers of P/L by a suitable sequence of consecutive cancellations. We extend this result to any ideal I in a regular local ring (R, n). To this purpose we have to consider more general kinds of cancellations. The connection between the graded perspective and the local one is a new viewpoint, and we hope it will be useful for studying the numerical invariants of classes of local rings.

Consecutive cancellations in Betti numbers of local rings

ROSSI, MARIA EVELINA;
2010-01-01

Abstract

Let I be a homogeneous ideal in a polynomial ring P over a field. By Macaulay’s Theorem there exists a lexicographic ideal L = Lex(I) with the same Hilbert function of I. Irena Peeva has proved that the Betti numbers of P/I can be obtained from the graded Betti numbers of P/L by a suitable sequence of consecutive cancellations. We extend this result to any ideal I in a regular local ring (R, n). To this purpose we have to consider more general kinds of cancellations. The connection between the graded perspective and the local one is a new viewpoint, and we hope it will be useful for studying the numerical invariants of classes of local rings.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/224928
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 12
social impact