相关论文: Monomial ideals with linear upper bound regularity

In this paper, we study ideals $I$ whose linear strand can be supported on a regular CW complex. We provide a sufficient condition for the linear strand of an arbitrary subideal of $I$ to remain supported on an easily described subcomplex.…

We determine the Castelnuovo-Mumford regularity of binomial edge ideals of complement reducible graphs (cographs). For cographs with $n$ vertices the maximum regularity grows as $2n/3$. We also bound the regularity by graph theoretic…

We show that the Castelnuovo-Mumford regularity of the binomial edge ideal of a graph is bounded below by the length of its longest induced path and bounded above by the number of its vertices.

We consider ideals in the ring $\mathbb{Z}_2[x_1,\ldots, x_n]$ that contain the polynomials $x_i^2 - x_i$ for $i = 1, \ldots, n$ and give various results related to the one-to-one correspondence between these ideals and the subsets of…

Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and $I$ be a monomial ideal generated in degree $d$. Bandari and Herzog conjectured that a monomial ideal $I$ is polymatroidal if and only if all its monomial…

We prove a uniform bound on the growth of symbolic powers of arbitrary (not necessarily radical) ideals in arbitrary (not necessarily excellent) regular rings of all characteristics. This gives a complete answer to a question of Hochster…

We prove that the Eliahou-Kervaire resolution of a Cohen-Macaulay stable monomial is supported by a regular CW complex whose underlying space is a closed ball. We also show that the modified Eliahou-Kervaire resolutions of variants of a…

The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the…

We characterize componentwise linear monomial ideals with minimal Taylor resolution and consider the lower bound for the Betti numbers of componentwise linear ideals.

We study ideal-theoretic conditions for a monomial ideal to be Golod. For ideals in a polynomial ring in three variables, our criteria give a complete characterization. Over such rings, we show that the product of two monomial ideals is…

In 2017, Cooper et al. proposed a conjecture providing a lower bound for the Waldschmidt constant of monomial ideals. We confirm this conjecture for some classes of monomial ideals. Recently, M\'endez, Pinto, and Villarreal formulated a…

We will give an upper bound for the $k$-normality of very ample lattice simplices, and then give an Eisenbud-Goto-type bound for some special classes of projective toric varieties.

We use the theory of poset resolutions to construct the minimal free resolution of an arbitrary stable monomial ideal in the polynomial ring whose coefficients are from a field. This resolution is recovered by utilizing a poset of…

We give a sharp lower bound for the Hilbert function in degree $d$ of artinian quotients $\Bbbk[x_1,\ldots,x_n]/I$ failing the Strong Lefschetz property, where $I$ is a monomial ideal generated in degree $d \geq 2$. We also provide sharp…

We determine, in a polynomial ring over a field, the arithmetical rank of certain ideals generated by a set of monomials and one binomial.

We introduce the notion of a Betti-linear monomial ideal, which generalizes the notion of lattice-linear monomial ideal introduced by Clark. We provide a characterization of Betti-linearity in terms of Tchernev's poset construction. As an…

In this paper we use some results related to regularity, Betti numbers and reduction of generic initial ideals, showing their stability in passing from an ideal to its initial ideal if the last has some simple properties.

For a monomial ideal $I$, let $G(I)$ be its minimal set of monomial generators. If there is a total order on $G(I)$ such that the corresponding Lyubeznik resolution of $I$ is a minimal free resolution of $I$, then $I$ is called a Lyubeznik…

In 2016, Ananyan and Hochster gave the first proof of a positive answer to Stillman's Question, which asked for a bound on the projective dimension of a graded polynomial ideal purely in terms of the number and degrees of its generators.…

We study the problem of $d$-gonality of the modular curve $X_0(N)$. As a result, we can give an upperbound of the level $N$ by means of $d$. This generalizes Ogg's result on hyperelliptic modular curves ($d = 2$). As a corollary of this…