科研之友
微信
新浪微博
Facebook
分享链接
摘要
Let K be an algebraically closed field. There has been much interest in characterizing multiple structures in P-K(n) defined on a linear subspace of small codimension under additional assumptions (e.g. Cohen-Macaulay). We show that no such finite characterization of multiple structures is possible if one only assumes unmixedness. Specifically, we prove that for any positive integers h, e >= 2 with (h, e) not equal (2,2) and p >= 5 there is a homogeneous ideal I in a polynomial ring over K such that (1) the height of I is h, (2) the Hilbert-Samuel multiplicity of R/I is e, (3) the projective dimension of R/I is at least p and (4) the ideal I is primary to a linear prime (x(1), ..., x(h)). This result is in stark contrast to Manolache's characterization of Cohen-Macaulay multiple structures in codimension 2 and multiplicity at most 4 and also to Engheta's characterization of unmixed ideals of height 2 and multiplicity 2.
- 出版日期2016-2-1
