Search results for "Primary decomposition"
showing 2 items of 2 documents
On the regularity and defect sequence of monomial and binomial ideals
2018
When S is a polynomial ring or more generally a standard graded algebra over a field K, with homogeneous maximal ideal m, it is known that for an ideal I of S, the regularity of powers of I becomes eventually a linear function, i.e., reg(Im) = dm + e for m ≫ 0 and some integers d, e. This motivates writing reg(Im) = dm + em for every m ⩾ 0. The sequence em, called the defect sequence of the ideal I, is the subject of much research and its nature is still widely unexplored. We know that em is eventually constant. In this article, after proving various results about the regularity of monomial ideals and their powers, we give several bounds and restrictions on em and its first differences when…
Tower sets and other configurations with the Cohen-Macaulay property
2014
Abstract Some well-known arithmetically Cohen–Macaulay configurations of linear varieties in P r as k-configurations, partial intersections and star configurations are generalized by introducing tower schemes. Tower schemes are reduced schemes that are a finite union of linear varieties whose support set is a suitable finite subset of Z + c called tower set. We prove that the tower schemes are arithmetically Cohen–Macaulay and we compute their Hilbert function in terms of their support. Afterwards, since even in codimension 2 not every arithmetically Cohen–Macaulay squarefree monomial ideal is the ideal of a tower scheme, we slightly extend this notion by defining generalized tower schemes …