I. García-Marco

activity

20142026

most citedAlgebraic invariants of projective monomial curves associated to generalized arithmetic sequences

15 citations · 20 across the 10 of their papers we have counts for

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math.AC2026

A note on strong affine semigroups

I. García-Marco, R. Tapia-Ramos, A. Vigneron-Tenorio

This work introduces and studies strong affine semigroups, extending the notion of strong numerical semigroups to the higher-dimensional setting. We show that non-numerical strong…

math.AC2026

Generalized Andrásfai graphs and special Betti diagrams of edge ideals

Sara Asensio, Ignacio García-Marco, Philippe Gimenez

Edge ideals of graphs were introduced by Villarreal in 1990, and have been the subject of many studies since then. In the same year, Fröberg characterized edge ideals with regulari…

math.AC2026

Castelnuovo-Mumford regularity of toric varieties with at most one singular point

Ignacio García-Marco, Philippe Gimenez, Mario González-Sánchez

We establish upper bounds for the Castelnuovo--Mumford regularity of the coordinate ring of a simplicial projective toric variety with at most one singular point. In the smooth cas…

math.AC2023

Universally free numerical semigroups

Ignacio García Marco, Pedro A. García-Sánchez, Ignacio Ojeda +1

A numerical semigroup is said to be universally free if it is free for any possible arrangement of its minimal generating set. In this work, we establish that toric ideals associat…

math.AC2017

On the linear independence of shifted powers

Ignacio García-Marco, Pascal Koiran, Timothée Pecatte

We call shifted power a polynomial of the form $(x - a)^{e}$ . The main goal of this paper is to obtain broadly applicable criteria ensuring that the elements of a finite family $F$ of…

math.AC2015★ 15 cited

Algebraic invariants of projective monomial curves associated to generalized arithmetic sequences

Isabel Bermejo, Eva García-Llorente, Ignacio García-Marco

Let $K$ be an infinite field and let $m_{1}, \dots, m_{n}$ be a generalized arithmetic sequence of positive integers, i.e., there exist $h, d, m_{1} \in Z^{+}$ such that $m_i = h m_…

math.AC2014

Matroid toric ideals: complete intersection, minors and minimal systems of generators

Ignacio García-Marco, Jorge Luis Ramírez Alfonsín

In this paper, we investigate three problems concerning the toric ideal associated to a matroid. Firstly, we list all matroids $M$ such that its corresponding toric ideal…

math.AC2014

Complete intersections in certain affine and projective monomial curves

I. Bermejo, I. García-Marco

Let $k$ be an arbitrary field, the purpose of this work is to provide families of positive integers $A = {d_{1}, \dots, d_{n}}$ such that either the toric ideal $I_{\mathcal…