1,721,000 research outputs found
Consecutive cancellations in Betti numbers of local rings
No full textLet 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
The structure of the Sally module of integrally closed ideals
No full textThe first two Hilbert coecients of a primary ideal play an important role in commutative algebra and in algebraic geometry. In this paper we give a complete algebraic structure of the Sally module of integrally closed ideals I in a Cohen Macaulay local ring A satisfying the equality e1(I) = e0(I) +l(A/I) + l(I2/QI) + 1 where Q is a minimal reduction of I, and e0(I) and e1(I) denote the rst two Hilbert coecients of I; respectively, the multiplicity and the Chern number of I. This almost extremal value of e1(I) with respect to classical inequalities holds a complete description of the homological and the numerical invariants of the associated graded ring.
Examples are given
- …
