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Teresa Cortadellas Benitez

Publications and source records attributed to Teresa Cortadellas Benitez.

10 recordsLinked to original sources
arXiv2025

On the effective Pourchet's Theorem

With the aid of Hensel Lemma, we refine the 2-adic Newton polygon algorithm proposed by Magron, Koprowski, and Vaccon at ISSAC 2023 to express computationally a given positive univariate polynomial with rational coefficients as a sum of five squares of rational polynomials -the effective Pourchet's Theorem- and extend it to cover almost all the possible inputs. We also provide examples which are covered with our methods but cannot be detected by previous conjectural algorithms.

math.NT↗
arXiv2021

Bounds for degrees of syzygies of polynomials defining a grade two ideal

We make explicit the exponential bound on the degrees of the polynomials appearing in the Effective Quillen-Suslin Theorem, and apply it jointly with the Hilbert-Burch Theorem to show that the syzygy module of a sequence of m polynomials in n variables defining a complete intersection ideal of grade two is free, and that a basis of it can be computed with bounded degrees. In the known cases, these bounds improve previous results.

math.AC↗
arXiv2019

Minimal solutions of the rational interpolation problem

We explore connections between the approach of solving the rational interpolation problem via resolutions of ideals and syzygies with the standard method provided by the Extended Euclidean Algorithm. As a consequence, we obtain explicit descriptions for solutions of "minimal" degrees in terms of the degrees of elements appearing in the EEA. This allows us to describe the minimal degree in a $μ$-basis of a polynomial planar parametrization in terms of a "critical" degree arising in the EEA.

math.AC↗
arXiv2019

The Rees Algebra of Parametric Curves via liftings

We study the defining equations of the Rees algebra of ideals arising from curve parametrizations in the plane and in rational normal scrolls, inspired by the work of Madsen and Kustin, Polini and Ulrich. The curves are related by work of Bernardi, Gimigliano and Ida, and we use this framework to relate the defining equations.

math.AC↗
arXiv2014

The Rees Algebra of a monomial plane parametrization

We compute a minimal bigraded resolution of the Rees Algebra associated to a proper rational parametrization of a monomial plane curve. We describe explicitly both the bigraded Betti numbers and the maps of the resolution in terms of a generalized version of the Euclidean Algorithm. We also explore the relation between pencils of adjoints of the monomial plane curve and elements in a suitable piece of the defining ideal of the Rees Algebra.

math.AC↗
arXiv2012

Rational plane curves parameterizable by conics

We introduce the class of rational plane curves parameterizable by conics as an extension of the family of curves parameterizable by lines (also known as monoid curves). We show that they are the image of monoid curves via suitable quadratic transformations in projective plane. We also describe all the possible proper parameterizations of them, and a set of minimal generators of the Rees Algebra associated to these parameterizations, extending well-known results for curves parameterizable by lines.

math.AG↗
arXiv2010

Minimal generators of the defining ideal of the Rees Algebra associated to monoid parametrizations

We describe a minimal set of generators of the defining ideal of the Rees Algebra associated to a proper parametrization of any monoid hypersurface. In the case of plane curves, we recover a known description for rational parametrizations having a syzygy of minimal degree (μ=1). We also show that our approach can be applied to parametrizations of rational surfaces having a Hilbert-Burch resolution with μ_1=μ_2=1.

math.AC↗
arXiv2009

Tangent cones of numerical semigroup rings

In this paper we describe the structure of the tangent cone of a numerical semigroup ring $A=k[[S]] \subseteq k[[t]]$ with multiplicity $e$ (as a module over the Noether normalization determined by the fiber cone of the ideal generated by $t^e$) in terms of some classical invariants of the corresponding numerical semigroup. Explicit computations are also made by using the GAP system.

math.AC↗