Related papers: Characterizations of freeness for equidimensional …

Given a finitely generated module $M$ over a Noetherian local ring $R$, we give a characterization for the first syzygy of the associated graded module $G_{\mathfrak{m}}(M)$ to be equigenerated. As an application of this, we identify a…

The primary goal of this paper is to investigate the structure of irreducible monomorphisms to and irreducible epimorphisms from finitely generated free modules over a noetherian local ring. Then we show that over such a ring,…

In this article, we study the quasi-homogeneity of a superpotential in a complete free algebra over an algebraic closed field of characteristic zero. We prove that a superpotential with finite dimensional Jacobi algebra is right equivalent…

Let A be a generic hyperplane arrangement composed of r hyperplanes in an n-dimensional vector space, and S the polynomial ring in n variables. We consider the S-submodule D(m)(A) of the nth Weyl algebra of homogeneous differential…

The focus of this article is the study of a certain type of singularities and their transfer properties in a universally equidimensional morphism (i.e. an open morphism with constant pure-dimensional fibers). The singularities of interest…

We construct a minimal free resolution of the semigroup ring k[C] in terms of minimal resolutions of k[A] and k[B] when <C> is a numerical semigroup obtained by gluing two numerical semigroups <A> and <B>. Using our explicit construction,…

This work concerns finite free complexes with finite length homology over a commutative noetherian local ring $R$. The focus is on complexes that have length $\mathrm{dim}\, R$, which is the smallest possible value, and in particular on…

We study monomial ideals with linear presentation or partially linear resolution. We give combinatorial characterizations of linear presentation for square-free ideals of degree 3, and for primary ideals whose resolutions are linear except…

We prove a generic flatness result for the cohomology of thickenings of a projective scheme that is smooth over a Noetherian domain containing a field of characteristic zero. Our study is motivated, in part, by a classical question in…

We use filtered log-$\mathscr{D}$-modules to represent the (dual) localization of Saito's Mixed Hodge Modules along a smooth hypersurface, and show that they also behave well under the direct image functor and the dual functor in the…

In the theory of persistent homology, a well known duality relates the barcodes of the absolute homology and relative cohomology of a one-parameter simplicial filtration. Motivated by the problem of computing free presentations of the…

We define logarithmic tangent sheaves associated with complete intersections in connection with Jacobian syzygies and distributions. We analyse the notions of local freeness, freeness and stability of these sheaves. We carry out a complete…

We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincar\'e series of the modules of…

Let $I$ be a graded ideal of $K[x_1,\ldots,x_n]$ generated by homogeneous polynomials of a same degree $d$, and assume that $I$ has linear quotients. In this note, we use Horseshoe Lemma to give a relatively direct inductive construction of…

Over a regular local ring of dimension two with maximal ideal m, we study the Buchsbaum-Rim multiplicity of a finitely generated module M of finite colength in a free module F. First, we investigate the colength of an m-primary ideal and…

Let $M$ be a finitely generated module over a local ring $(R,\mathfrak{m})$. By $\mathcal{S}_j(M)$, we denote the $j$th symmetric power of $M$ ($j$th graded component of the symmetric algebra $\mathcal{S}_R(M)$). The purpose of this paper…

Let $k$ be a field with characteristic zero, $R$ be the ring $k[x_1, \cdots, x_n]$ and $I$ be a monomial ideal of $R$. We study the Artinian local algebra $R/I$ when considered as an $R$-module $M$. We show that the largest reduced…

We study the positivity of CM line bundles on the coarse moduli space of Kawamata log terminal (klt) good minimal models with Kodaira dimension one. We prove that the seminormalization of the moduli space is quasi-projective under a mild…

This paper introduces two new notions of graded linear resolution and graded linear quotients, which generalize the concepts of linear resolution property and linear quotient for modules over the polynomial ring $A=k[x_1, \dots ,x_n]$.…

In this paper, we study the Kauffman bracket skein module of closed oriented three-manifolds at a non-multiple-of-four roots of unity. Our main result establishes that the localization of this module at a maximal ideal, which corresponds to…