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Haydee Lindo

Publications and source records attributed to Haydee Lindo.

11 recordsLinked to original sources
arXiv2026

Trace ideals of syzygies

We study the behavior of trace ideals under taking syzygies. In particular, when $R$ is numerical semigroup ring and $I$ is a homogeneous ideal in $R$, we obtain an upper estimate for $\operatorname{tr}_R(\Omega^1_R(I))$, and we show this estimate is sharp when $I$ is the conductor ideal $\mathfrak{c}_R$ of $R$. Using this result, we characterize the numerical semigroup rings for which $\operatorname{tr}_R(M) \subseteq \operatorname{tr}_R(\Omega^1_R(M))$ holds for every finitely generated $R$-module $M$. In a similar vein, we characterize numerical semigroup rings for which $\operatorname{tr}_R(\Omega^1_R(\mathfrak{c}_R))=\mathfrak{c}_R$.

math.AC↗
arXiv2026

Shuffling the Deck: Invariant Theory and the Graph Reconstruction Conjecture

The graph reconstruction conjecture asserts that every simple graph on at least three vertices is uniquely determined by its deck of vertex-deleted subgraphs. In this expository article we survey the conjecture and present an invariant-theoretic approach to studying it. The aim is to be able to show that polynomials that distinguish between decks also distinguish between original graphs, thus translating a graph-theoretic problem into an algebraic one.

math.CO↗
arXiv2026

Gorenstein Special Fiber Rings of Ladder Determinantal Modules

A ladder determinantal module is an arbitrary direct sum of ideals of maximal minors of a generic ladder matrix. In this article, we give necessary and sufficient conditions for the special fiber ring of such modules to be Gorenstein. These conditions are expressed in terms of data obtained from the underlying matrix.

math.AC↗
arXiv2025

Trace does not preserve Reflexivity

In this note, we address a question raised in a recent work by Dao-Maitra-Sridhar, regarding the preservation of reflexivity under taking trace. We answer this question negatively. We also study a few cases where the question has a positive answer in a one dimensional, analytically unramified Cohen-Macaulay local ring.

math.AC↗
arXiv2025

Algebraic invariants of the special fiber ring of ladder determinantal modules

We provide explicit formulas for key invariants of special fiber rings of ladder determinantal modules, that is, modules that are direct sums of ideals of maximal minors of a ladder matrix. Our results are given in terms of the combinatorial data of the associated ladder matrix. In particular, we compute its dimension, regularity, $a$-invariant, and multiplicity, which via \textsc{Sagbi} degeneration coincide with those of Hibi rings associated to a distributive lattice. Then, via Gr\"{o}bner degeneration these calculations are reduced to quotients of polynomial rings by monomial ideals. Our formula for the multiplicity of the special fiber ring of these ladder determinantal modules is obtained by counting the number of standard skew Young tableaux associated to a certain skew partition, and so provides a natural generalization of the classical formula for the degree of the Grassmannian.

math.AC↗
arXiv2022

The trace property in preenveloping classes

We develop the theory of trace modules up to isomorphism and explore the relationship between preenveloping classes of modules and the property of being a trace module, guided by the question of whether a given module is trace in a given preenvelope. As a consequence we identify new examples of trace ideals and trace modules, and characterize several classes of rings with a focus on the Gorenstein and regular properties.

math.AC↗
arXiv2020

Canonical Resolutions over Koszul Algebras

We generalize Buchsbaum and Eisenbud's resolutions for the powers of the maximal ideal of a polynomial ring to resolve powers of the homogeneous maximal ideal over graded Koszul algebras. Our approach has the advantage of producing resolutions that are both more explicit and minimal compared to those previously discovered by Green and Mart\'{\i}nez-Villa \cite{GreenMartinezVilla} or Mart\'{\i}nez-Villa and Zacharia \cite{MartinezVillaZacharia}.

math.AC↗
arXiv2018

Trace Ideals and the Gorenstein Property

Let R be a local Noetherian commutative ring. We prove that R is an Artinian Gorenstein ring if and only if every ideal in R is a trace ideal. We discuss when the trace ideal of a module coincides with its double annihilator.

math.AC↗
arXiv2016

Trace Ideals and Centers of Endomorphism Rings of Modules over Commutative Rings

Let $R$ be a commutative Noetherian ring and $M$ a finitely generated $R$-module. Under various hypotheses, it is proved that the center of $\mbox{End}_R(M)$ coincides with the endomorphism ring of the trace ideal of $M$. These results are exploited to establish results for balanced and rigid modules, and to settle certain cases of a conjecture of Huneke and Wiegand.

math.AC↗