ﻻ يوجد ملخص باللغة العربية
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.
Building on previous work by the same authors, we show that certain ideals defining Gorenstein rings have expected resurgence, and thus satisfy the stable Harbourne Conjecture. In prime characteristic, we can take any radical ideal defining a Gorenst
Let $R$ be a polynomial ring over a field and $I subset R$ be a Gorenstein ideal of height three that is minimally generated by homogeneous polynomials of the same degree. We compute the multiplicity of the saturated special fiber ring of $I$. The ob
Let $R=Bbbk[x_1,dots,x_n]$ be a polynomial ring over a field $Bbbk$ and let $Isubset R$ be a monomial ideal preserved by the natural action of the symmetric group $mathfrak S_n$ on $R$. We give a combinatorial method to determine the $mathfrak S_n$-m
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 c
We graph-theoretically characterize triangle-free Gorenstein graphs $G$. As an application, we classify when $I(G)^2$ is Cohen-Macaulay.