相关论文: Ideals of general forms and the ubiquity of the We…

For a graded ideal I in a graded ring, the deviation of I is defined as the difference between the minimal number of generators of I and its grade. In this article, we provide bigraded free resolutions of the symmetric algebras for specific…

Let I be the ideal corresponding to a set of general points $p_1,...,p_n \in P^2$. There recently has been progress in showing that a naive lower bound for the Hilbert functions of symbolic powers $I^{(m)}$ is in fact attained when n>9.…

A set of polynomials G in a polynomial ring S over a field is said to be a universal Groebner basis, if G is a Groebner basis with respect to every term order on S. Twenty years ago Bernstein, Sturmfels, and Zelevinsky proved that the set…

We compute the generic initial ideal of a complete intersection of embedding dimension three with strong Lefschetz property and we show that it is an almost reverse lexicographic ideal. This enable us to give a proof for Moreno's conjecture…

We find a sufficient condition that $\H$ is not level based on a reduction number. In particular, we prove that a graded Artinian algebra of codimension 3 with Hilbert function $\H=(h_0,h_1,..., h_{d-1}>h_d=h_{d+1})$ cannot be level if…

Let N be a finitely generated module over a Noetherian local ring (R,m). We give criteria for the height of the order ideal N^*(x) of an element x \in N to be bounded by the rank of N. The Generalized Principal Ideal Theorem of Bruns,…

Let $R$ be a polynomial ring in $N$ variables over an arbitrary field $K$ and let $I$ be an ideal of $R$ generated by $n$ polynomials of degree at most 2. We show that there is a bound on the projective dimension of $R/I$ that depends only…

Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal $I$ in $\loneg$, the space of radial integrable functions on $G=SU(1,1)$, so that $I=\loneg$ or $I=\lonez$---the ideal of…

Let $(R,\mathfrak{m})$ be a Noetherian local ring of prime characteristic $p$ and $Q$ be an $\mathfrak{m}$-primary parameter ideal. We give criteria for F-rationality of $R$ using the tight Hilbert function $H^*_Q(n)=\ell(R/(Q^n)^*$ and the…

A homogeneous ideal $I$ of a polynomial ring $S$ is said to have the Rees property if, for any homogeneous ideal $J \subset S $ which contains $I$, the number of generators of $J$ is smaller than or equal to that of $I$. A homogeneous ideal…

Let C be a uniform clutter, i.e., all the edges of C have the same size, and let A be the incidence matrix of C. We denote the column vectors of A by v1,...,vq. The vertex covering number of C, denoted by g, is the smallest number of…

We introduce positive Gorenstein ideals. These are Gorenstein ideals in the graded ring $\RR[x]$ with socle in degree 2d, which when viewed as a linear functional on $\RR[x]_{2d}$ is nonnegative on squares. Equivalently, positive Gorenstein…

Let $\mathbf{k}$ be a field which is either finite or algebraically closed and let $R = \mathbf{k}[x_1,\ldots,x_n].$ We prove that any $g_1,\ldots,g_s\in R$ homogeneous of positive degrees $\le d$ are contained in an ideal generated by an…

Let $R$ be a finite commutative ring with identity, and let $P$ be a proper prime ideal of $R$. The prime ideal graph $\Gamma_P(R)$ has vertex set of $R\setminus\{0\}$, where two distinct vertices $x$ and $y$ are adjacent if and only if…

In this paper we define and explore properties of mixed multiplicities of (not necessarily Noetherian) filtrations of $m_R$-primary ideals in a Noetherian local ring $R$, generalizing the classical theory for $m_R$-primary ideals. We…

Let $M$ be a finitely generated module of dimension $d$ and depth $t$ over a Noetherian local ring ($A, {\mathfrak m}$) and $I$ an ${\mathfrak m}$-primary ideal. In the main result it is shown that the last $t$ Hilbert coefficients…

Let $K$ be a number field with ring of integers $\mathcal{O}$ and $\alpha\in\mathcal{O}$. For any prime ideal $\mathfrak{p}$ of $\mathcal{O}$, we obtain its higher $\alpha$-Wieferich property, which implies a nonexistence theorem for higher…

For projective Reed--Muller-type codes we give a global duality criterion in terms of the v-number and the Hilbert function of a vanishing ideal. As an application, we provide a global duality theorem for projective Reed--Muller-type codes…

In this article, we study the density conjecture of Katz and Sarnak for $L$-functions of ad\'elic Hilbert modular forms and their convolutions. In particular, under the generalised Riemann hypothesis, we establish several instances…

The vanishing ideal I of a subspace arrangement is an intersection of linear ideals. We give a formula for the Hilbert polynomial of I if the subspaces meet transversally. We also give a formula for the Hilbert series of a product J of the…