Searcharxiv⌕ Search

arXiv subjects

Yi-Huang Shen

Publications and source records attributed to Yi-Huang Shen.

At least 19 recordsLinked to original sources
arXiv2026

The $v$-number of generalized binomial edge ideals of some graphs

Let $G$ be a finite connected simple graph, and let $\mathcal{J}_{K_m,G}$ denote its generalized binomial edge ideal. By investigating the colon ideals of $\mathcal{J}_{K_m,G}$, we derive a formula for the local $\mathrm{v}$-number of $\mathcal{J}_{K_m,G}$ with respect to the empty cut set. Furthermore, we classify graphs for which this generalized binomial edge ideal has $\mathrm{v}$-numbers $1$ or $2$. When $G$ is a connected closed graph, we compute the local $\mathrm{v}$-number of $\mathcal{J}_{K_2,G}$ by generalizing the work of Dey et al. Additionally, under the condition that $G$ is Cohen--Macaulay, we derive formulas for the $\mathrm{v}$-number of $\mathcal{J}_{K_m,G}$ and $\mathcal{J}_{K_2,G}^k$, and show that the $\mathrm{v}$-number of $\mathcal{J}_{K_2,G}^k$ is a linear function of $k$.

math.AC↗
arXiv2025

Binomial edge rings associated to skew Ferrers diagrams

In this study, we investigate the binomial edge ring associated with the skew Ferrers diagram. By employing Sagbi basis theory, we construct a quadratic Gröbner basis for its defining ideal. As an application, we prove that this ring is a Koszul, Cohen-Macaulay, normal domain. Moreover, we precisely determine its Krull dimension.

math.AC↗
arXiv2025

Regularity and multiplicity of Veronese type algebras

In this paper, we study the algebra of Veronese type. We show that the presentation ideal of this algebra has an initial ideal whose Alexander dual has linear quotients. As an application, we explicitly obtain the Castelnuovo-Mumford regularity of the Veronese type algebra. Furthermore, we give an effective upper bound on the multiplicity of this algebra.

math.AC↗
arXiv2025

Blowup algebras of determinantal modules

We study the blowup algebras of the modules that are direct sums of ideals generated by either maximal minors of a ladder matrix or unit interval determinantal ideals. Specifically, we determine Gröbner bases for the presentation ideals of multi-Rees algebras and their special fiber rings. Our analysis reveals that the multi-blowup algebras are Koszul Cohen--Macaulay normal domains, possess rational singularities in characteristic zero, and are F-rational in positive characteristic.

math.AC↗
arXiv2025

Blowup Algebras of $n$--dimensional Ferrers Diagrams

We demonstrate that the direct sum of ideals satisfying the strong $\ell$-exchange property is of fiber type. Furthermore, we provide Gröbner bases of the presentation ideals of multi-Rees algebras and the corresponding special fibers, when they are associated with an $n$-dimensional Ferrers diagram that is standardizable. In particular, we show that these blowup algebras are Koszul Cohen--Macaulay normal domains and classify their singularities.

math.AC↗
arXiv2023

Generalized binomial edge ideals of complete $r$-partite graphs

This paper analyzes the cohomological dimension of the generalized binomial edge ideal $\calJ_{K_m,G}$ for a complete $r$-partite graph $G$. Additionally, the Krull dimension, the depth, the Castelnuovo--Mumford regularity, the Hilbert series, and the multiplicity of its quotient ring are explicitly determined.

math.AC↗
arXiv2023

Powers of generalized binomial edge ideals of path graphs

In this article, we study the powers of the generalized binomial edge ideal $\mathcal{J}_{K_m,P_n}$ of a path graph $P_n$. We explicitly compute their regularities and determine the limit of their depths. We also show that these ordinary powers coincide with their symbolic powers. Additionally, we study the Rees algebra and the special fiber ring of $\mathcal{J}_{K_m,P_n}$ via Sagbi basis theory. In particular, we obtain exact formulas for the regularity of these blowup algebras.

math.AC↗
arXiv2023

Generalized binomial edge ideals of bipartite graphs

Connected bipartite graphs whose binomial edge ideals are Cohen--Macaulay have been classified by Bolognini et al. In this paper, we compute the depth, Castelnuovo--Mumford regularity, and dimension of the generalized binomial edge ideals of these graphs.

math.AC↗
arXiv2022

Regularity and multiplicity of toric rings of three-dimensional Ferrers diagrams

We investigate the Castelnuovo-Mumford regularity and the multiplicity of the toric ring associated with a three-dimensional Ferrers diagram. In particular, in the rectangular case, we provide direct formulas for these two important invariants. Then, we compare these invariants for an accompanying pair of Ferrers diagrams under some mild conditions and bound the Castelnuovo-Mumford regularity for more general cases.

math.AC↗
arXiv2021

Regularity of powers of (parity) binomial edge ideals

In this paper, we provide exact formulas for the Castelnuovo-Mumford regularity of powers of an almost complete intersection ideal $I$ which is generated by a homogeneous $d$-sequence. As applications, when $I$ is an almost complete intersection, taking the form of the (parity) binomial edge ideal of a connected graph, we can describe explicitly formulas for $\reg(I^t)$ for $t\ge 2$. The only exception is when $I$ is the parity binomial edge ideal of a graph which is obtained by adding an edge between two disjoint odd cycles.

math.AC↗
arXiv2021

Fiber cones of rational normal scrolls are Cohen-Macaulay

In this short paper, we show that the fiber cones of rational normal scrolls are Cohen-Macaulay. As an application, we compute their Castelnuovo-Mumford regularities and $\mathbf{a}$-invariants, as well as the reduction number of the defining ideals of the rational normal scrolls. We also characterize the Gorensteinness of the fiber cone.

math.AC↗
arXiv2021

Blow-up algebras of secant varieties of rational normal scrolls

In this paper, we are mainly concerned with the blow-up algebras of the secant varieties of balanced rational normal scrolls. In the first part, we give implicit defining equations of their associated Rees algebras and fiber cones. Consequently, we can tell that the fiber cones are Cohen--Macaulay normal domains. Meanwhile, these fiber cones have rational singularities in characteristic zero, and are $F$-rational in positive characteristic. The Gorensteinness of the fiber cones can also be characterized. In the second part, we compute the Castelnuovo--Mumford regularities and $\mathbf{a}$-invariants of the fiber cones. We also present the reduction numbers of the ideals defined by the secant varieties.

math.AC↗
arXiv2021

Symbolic powers of generalized star configurations of hypersurfaces

We introduce the class of sparse symmetric shifted monomial ideals. These ideals have linear quotients and their Betti numbers are computed. Using this, we prove that the symbolic powers of the generalized star configuration ideal are sequentially Cohen--Macaulay under some mild genericness assumption. With respect to these symbolic powers, we also consider the Harbourne--Huneke containment problem and establish the Demailly-like bound.

math.AC↗
arXiv2020

$a_i$-invariants of powers of ideals

Inspired by the recent work of Lu and O'Rourke, we study the $a_i$-invariants of (symbolic) powers of some graded ideals. The first scenario is when $I$ and $J$ are two graded ideals in two distinct polynomial rings $R$ and $S$ over a common field $\mathbb{K}$. We study the $a_i$-invariants of the powers of the fiber product via the corresponding knowledge of $I$ and $J$. The second scenario is when $I_Δ$ is the Stanley-Reisner ideal of a $k$-dimensional simplicial complex $Δ$ with $k\ge 2$. We investigate the $a_i$-invariants of the symbolic powers of $I_Δ$.

math.AC↗
arXiv2019

Symbolic powers and free resolutions of generalized star configurations of hypersurfaces

As a generalization of the ideals of star configurations of hypersurfaces, we consider the $a$-fold product ideal $I_a(f_1^{m_1}\cdots f_s^{m_s})$ when ${f_1,\dots,f_s}$ is a sequence of generic forms and $1\le a\le m_1+\cdots+m_s$. Firstly, we show that this ideal has complete intersection quotients when these forms are of the same degree and essentially linear. Then we study its symbolic powers while focusing on the uniform case with $m_1=\cdots=m_s$. For large $a$, we describe its resurgence and symbolic defect. And for general $a$, we also investigate the corresponding invariants for meeting-at-the-minimal-components version of symbolic powers.

math.AC↗
arXiv2019

Generalized Newton Complementary Duals of Monomial Ideals

Given a monomial ideal in a polynomial ring over a field, we define the generalized Newton complementary dual of the given ideal. We show good properties of such duals including linear quotients and isomorphisms between the special fiber rings. We construct the cellular free resolutions of duals of strongly stable ideals generated in the same degree. When the base ideal is generated in degree two, we provide an explicit description of cellular free resolution of the dual of a compatible generalized stable ideal.

math.AC↗
arXiv2018

Koszul blowup algebras associated to three-dimensional Ferrers diagrams

We investigate the Rees algebra and the toric ring of the squarefree monomial ideal associated to the three-dimensional Ferrers diagram. Under the projection property condition, we describe explicitly the presentation ideals of the Rees algebra and the toric ring. We show that the toric ring is a Koszul Cohen--Macaulay normal domain, while the Rees algebra is Koszul and the defining ideal is of fiber type.

math.AC↗