Betti numbers of powers of ideals

  • Gioia Failla University of Messina
  • Monica La Barbiera University of Messina
  • Paola L. Staglianò University of Messina
Keywords: Betti numbers, Rees algebra, Primary ideals

Abstract

Let A=K[x1, ..... ,xn] be a standard graded polynomial ring over a field K, let M = (x_1, .... , x_n) be the graded maximal ideal and I a graded ideal of A. For each i the Betti numbers b_i(I^k ) of I^k are polynomial functions for k>>0. We show that if I is M-primary, then these polynomial functions have the same degree for all i .

Author Biographies

Gioia Failla, University of Messina
Department of Mathematics
C.da Papardo, salita Sperone, 31
98166 Messina, Italy
Monica La Barbiera, University of Messina
Department of Mathematics
C.da Papardo, salita Sperone, 31
98166 Messina, Italy
Paola L. Staglianò, University of Messina
Department of Mathematics
C.da Papardo, salita Sperone, 31
98166 Messina, Italy
Published
2009-04-07
Section
Articoli