ترغب بنشر مسار تعليمي؟ اضغط هنا

Classes of sequentially Cohen-Macaulay squarefree monomial ideals

214   0   0.0 ( 0 )
 نشر من قبل Olteanu Anda Georgiana
 تاريخ النشر 2011
  مجال البحث
والبحث باللغة English
 تأليف Oana Olteanu




اسأل ChatGPT حول البحث

We compute the minimal primary decomposition for completely squarefree lexsegment ideals. We show that critical squarefree monomial ideals are sequentially Cohen-Macaulay. As an application, we give a complete characterization of the completely squarefree lexsegment ideals which are sequentially Cohen-Macaulay and we also derive formulas for some homological invariants of this class of ideals.



قيم البحث

اقرأ أيضاً

303 - Ezra Miller 2008
Scattered over the past few years have been several occurrences of simplicial complexes whose topological behavior characterize the Cohen-Macaulay property for quotients of polynomial rings by arbitrary (not necessarily squarefree) monomial ideals. T he purpose of this survey is to gather the developments into one location, with self-contained proofs, including direct combinatorial topological connections between them.
For a partition $lambda$ of $n in {mathbb N}$, let $I^{rm Sp}_lambda$ be the ideal of $R=K[x_1,ldots,x_n]$ generated by all Specht polynomials of shape $lambda$. In the previous paper, the second author showed that if $R/I^{rm Sp}_lambda$ is Cohen-Ma caulay, then $lambda$ is either $(n-d,1,ldots,1),(n-d,d)$, or $(d,d,1)$, and the converse is true if ${rm char}(K)=0$. In this paper, we compute the Hilbert series of $R/I^{rm Sp}_lambda$ for $lambda=(n-d,d)$ or $(d,d,1)$. Hence, we get the Castelnuovo-Mumford regularity of $R/I^{rm Sp}_lambda$, when it is Cohen-Macaulay. In particular, $I^{rm Sp}_{(d,d,1)}$ has a $(d+2)$-linear resolution in the Cohen-Macaulay case.
Let $S=K[x_1,ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and $Isubset S$ a squarefree monomial ideal. In the present paper we are interested in the monomials $u in S$ belonging to the socle $Soc(S/I^{k})$ of $S/I^{k}$, i.e., $u otin I^{k}$ and $ux_{i} in I^{k}$ for $1 leq i leq n$. We prove that if a monomial $x_1^{a_1}cdots x_n^{a_n}$ belongs to $Soc(S/I^{k})$, then $a_ileq k-1$ for all $1 leq i leq n$. We then discuss squarefree monomial ideals $I subset S$ for which $x_{[n]}^{k-1} in Soc(S/I^{k})$, where $x_{[n]} = x_{1}x_{2}cdots x_{n}$. Furthermore, we give a combinatorial characterization of finite graphs $G$ on $[n] = {1, ldots, n}$ for which $depth S/(I_{G})^{2}=0$, where $I_{G}$ is the edge ideal of $G$.
115 - Luca Amata , Marilena Crupi 2021
Let $K$ be a field and $S = K[x_1,dots,x_n]$ be a polynomial ring over $K$. We discuss the behaviour of the extremal Betti numbers of the class of squarefree strongly stable ideals. More precisely, we give a numerical characterization of the possible extremal Betti numbers (values as well as positions) of such a class of squarefree monomial ideals.
194 - Oana Olteanu 2011
In this thesis we are interested in describing some homological invariants of certain classes of monomial ideals. We will pay attention to the squarefree and non-squarefree lexsegment ideals.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا