اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn $p_g$-ideals
139
0
0.0
(
0
)
تأليف
Tony J. Puthenpurakal
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $(A,mathfrak{m})$ be an excellent normal domain of dimension two. We define an $mathfrak{m}$-primary ideal $I$ to be a $p_g$-ideal if the Rees algebra $A[It]$ is a Cohen-Macaulay normal domain. When $A$ contains an algebraically closed field $k cong A/mathfrak{m}$ then Okuma, Watanabe and Yoshida proved that $A$ has $p_g$-ideals and furthermore product of two $p_g$-ideals is a $p_g$ ideal. In this article we show that if $A$ is an excellent normal domain of dimension two containing a field $k cong A/mathfrak{m}$ of characteristic zero then also $A$ has $p_g$-ideals. Furthermore product of two $p_g$-ideals is $p_g$.
قيم البحث
اقرأ أيضاً
We define the notion of a power stable ideal in a polynomial ring $ R[X]$ over an integral domain $ R $. It is proved that a maximal ideal $chi$ $ M $ in $ R[X]$ is power stable if and only if $ P^t $ is $ P$- primary for all $ tgeq 1 $ for the prime
ideal $ P = M cap R $. Using this we prove that for a Hilbert domain $R$ any radical ideal in $R[X]$ which is a finite intersection G-ideals is power stable. Further, we prove that if $ R $ is a Noetherian integral domain of dimension 1 then any radical ideal in $ R[X] $ is power stable. Finally, it is proved that if every ideal in $ R[X]$ is power stable then $ R $ is a field.
Let $k$ be a field and $G subseteq Gl_n(k)$ be a finite group with $|G|^{-1} in k$. Let $G$ act linearly on $A = k[X_1, ldots, X_n]$ and let $A^G$ be the ring of invariants. Suppose there does not exist any non-trivial one-dimensional representation
of $G$ over $k$. Then we show that if $Q$ is a $G$-invariant homogeneous ideal of $A$ such that $A/Q$ is a Gorenstein ring then $A^G/Q^G$ is also a Gorenstein ring.
Jet schemes and arc spaces received quite a lot of attention by researchers after their introduction, due to J. Nash, and established their importance as an object of study in M. Kontsevichs motivic integration theory. Several results point out that
jet schemes carry a rich amount of geometrical information about the original object they stem from, whereas, from an algebraic point of view, little is know about them. In this paper we study some algebraic properties of jet schemes ideals of pfaffian varieties and we determine under which conditions the corresponding jet scheme varieties are irreducible.
We consider the fiber cone of monomial ideals. It is shown that for monomial ideals $Isubset K[x,y]$ of height $2$, generated by $3$ elements, the fiber cone $F(I)$ of $I$ is a hypersurface ring, and that $F(I)$ has positive depth for interesting cla
sses of height $2$ monomial ideals $Isubset K[x,y]$, which are generated by $4$ elements. For these classes of ideals we also show that $F(I)$ is Cohen--Macaulay if and only if the defining ideal $J$ of $F(I)$ is generated by at most 3 elements. In all the cases a minimal set of generators of $J$ is determined.
We characterize the graphs $G$ for which their toric ideals $I_G$ are complete intersections. In particular we prove that for a connected graph $G$ such that $I_G$ is complete intersection all of its blocks are bipartite except of at most two. We pro
ve that toric ideals of graphs which are complete intersections are circuit ideals. The generators of the toric ideal correspond to even cycles of $G$ except of at most one generator, which corresponds to two edge disjoint odd cycles joint at a vertex or with a path. We prove that the blocks of the graph satisfy the odd cycle condition. Finally we characterize all complete intersection toric ideals of graphs which are normal.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
