@article{cid-ruiz_polini_ulrich_2025, title={Generalized Jouanolou duality, weakly Gorenstein rings, and applications to blowup algebras}, journal={Journal für die reine und angewandte Mathematik (Crelle's journal)}, author={Cid-Ruiz, Yairon and Polini, Claudia and Ulrich, Bernd}, year={2025} }
@article{cid-ruiz_smirnov_2024, title={Effective generic freeness and applications to local cohomology}, url={http://dx.doi.org/10.1112/jlms.12995}, DOI={10.1112/jlms.12995}, abstractNote={Abstract Let be a Noetherian domain and be a finitely generated ‐algebra. We study several features regarding the generic freeness over of an ‐module. For an ideal , we show that the local cohomology modules are generically free over under certain settings where is a smooth ‐algebra. By utilizing the theory of Gröbner bases over arbitrary Noetherian rings, we provide an effective method to b make explicit the generic freeness over of a finitely generated ‐module.}, journal={Journal of the London Mathematical Society}, author={Cid-Ruiz, Yairon and Smirnov, Ilya}, year={2024}, month={Oct} }
@article{cid-ruiz_li_matherne_2024, title={Log-concavity of polynomials arising from equivariant cohomology}, journal={arXiv preprint arXiv:2411.17572}, author={Cid-Ruiz, Yairon and Li, Yupeng and Matherne, Jacob P}, year={2024} }
@article{cid-ruiz_polini_ulrich_2024, title={Multidegrees, families, and integral dependence}, journal={arXiv preprint arXiv:2405.07000}, author={Cid-Ruiz, Yairon and Polini, Claudia and Ulrich, Bernd}, year={2024} }
@article{cid-ruiz_mohammadi_monin_2024, title={Multigraded algebras and multigraded linear series}, volume={109}, ISSN={["1469-7750"]}, url={http://dx.doi.org/10.1112/jlms.12880}, DOI={10.1112/jlms.12880}, abstractNote={Abstract This paper is devoted to the study of multigraded algebras and multigraded linear series. For an ‐graded algebra , we define and study its volume function , which computes the asymptotics of the Hilbert function of . We relate the volume function to the volume of the fibers of the global Newton–Okounkov body of . Unlike the classical case of standard multigraded algebras, the volume function is not a polynomial in general. However, in the case when the algebra has a decomposable grading, we show that the volume function is a polynomial with nonnegative coefficients. We then define mixed multiplicities in this case and provide a full characterization for their positivity. Furthermore, we apply our results on multigraded algebras to multigraded linear series. Our work recovers and unifies recent developments on mixed multiplicities. In particular, we recover results on the existence of mixed multiplicities for (not necessarily Noetherian) graded families of ideals and on the positivity of the multidegrees of multiprojective varieties.}, number={3}, journal={JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES}, author={Cid-Ruiz, Yairon and Mohammadi, Fatemeh and Monin, Leonid}, year={2024}, month={Mar} }
@article{cid-ruiz_2024, title={Polar Multiplicities and Integral Dependence}, volume={7}, ISSN={["1687-0247"]}, url={http://dx.doi.org/10.1093/imrn/rnae163}, DOI={10.1093/imrn/rnae163}, abstractNote={Abstract We provide new criteria for the integrality and birationality of an extension of graded algebras in terms of the general notion of polar multiplicities of Kleiman and Thorup. As an application, we obtain a new criterion for when a module is a reduction of another in terms of certain mixed Buchsbaum–Rim multiplicities. Furthermore, we prove several technical results regarding polar multiplicities.}, journal={INTERNATIONAL MATHEMATICS RESEARCH NOTICES}, author={Cid-Ruiz, Yairon}, year={2024}, month={Jul} }
@article{cid-ruiz_2024, title={Relative mixed multiplicities and mixed Buchsbaum-Rim multiplicities}, journal={arXiv preprint arXiv:2311.15105}, author={Cid-Ruiz, Yairon}, year={2024} }
@article{cid-ruiz_jeffries_2024, title={Uniformity in nonreduced rings via Noetherian operators}, journal={arXiv preprint arXiv:2404.02057}, author={Cid-Ruiz, Yairon and Jeffries, Jack}, year={2024} }
@article{cid-ruiz_ramkumar_2023, title={A local study of the fiber-full scheme}, url={http://dx.doi.org/10.1016/j.jalgebra.2023.08.039}, DOI={10.1016/j.jalgebra.2023.08.039}, journal={Journal of Algebra}, author={Cid-Ruiz, Yairon and Ramkumar, Ritvik}, year={2023}, month={Dec} }
@article{cid-ruiz_clarke_mohammadi_2023, title={A study of nonlinear multiview varieties}, url={http://dx.doi.org/10.1016/j.jalgebra.2022.12.036}, DOI={10.1016/j.jalgebra.2022.12.036}, journal={Journal of Algebra}, author={Cid-Ruiz, Yairon and Clarke, Oliver and Mohammadi, Fatemeh}, year={2023}, month={Apr} }
@article{castillo_cid-ruiz_mohammadi_montaño_2023, title={Double Schubert polynomials do have saturated Newton polytopes}, url={http://dx.doi.org/10.1017/fms.2023.101}, DOI={10.1017/fms.2023.101}, abstractNote={Abstract We prove that double Schubert polynomials have the saturated Newton polytope property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are motivated by the theory of multidegrees. We introduce a notion of standardization of ideals that enables us to study nonstandard multigradings. This allows us to show that the support of the multidegree polynomial of each Cohen–Macaulay prime ideal in a nonstandard multigrading, and in particular, that of each Schubert determinantal ideal is a discrete polymatroid.}, journal={Forum of Mathematics, Sigma}, author={Castillo, Federico and Cid-Ruiz, Yairon and Mohammadi, Fatemeh and Montaño, Jonathan}, year={2023} }
@article{cid-ruiz_2023, title={Fiber-full modules and a local freeness criterion for local cohomology modules}, url={http://dx.doi.org/10.1007/s00209-022-03190-6}, DOI={10.1007/s00209-022-03190-6}, journal={Mathematische Zeitschrift}, author={Cid-Ruiz, Yairon}, year={2023}, month={Feb} }
@article{caminata_cid-ruiz_conca_2023, title={Multidegrees, prime ideals, and non-standard gradings}, url={http://dx.doi.org/10.1016/j.aim.2023.109361}, DOI={10.1016/j.aim.2023.109361}, journal={Advances in Mathematics}, author={Caminata, Alessio and Cid-Ruiz, Yairon and Conca, Aldo}, year={2023}, month={Dec} }
@article{cid-ruiz_2022, title={A D-modules approach on the equations of the Rees algebra}, url={http://dx.doi.org/10.1216/jca.2022.14.155}, DOI={10.1216/jca.2022.14.155}, journal={Journal of Commutative Algebra}, author={Cid-Ruiz, Yairon}, year={2022}, month={Jun} }
@article{cid-ruiz_montaño_2022, title={Convex bodies and graded families of monomial ideals}, url={http://dx.doi.org/10.4171/rmi/1373}, DOI={10.4171/rmi/1373}, abstractNote={We show that the mixed volumes of arbitrary convex bodies are equal to mixed multiplicities of graded families of monomial ideals, and to normalized limits of mixed multiplicities of monomial ideals. This result evinces the close relation between the theories of mixed volumes from convex geometry and mixed multiplicities from commutative algebra.}, journal={Revista Matemática Iberoamericana}, author={Cid-Ruiz, Yairon and Montaño, Jonathan}, year={2022}, month={Aug} }
@article{castillo_cid-ruiz_mohammadi_montaño_2022, title={K-polynomials of multiplicity-free varieties}, journal={arXiv preprint arXiv:2212.13091}, author={Castillo, Federico and Cid-Ruiz, Yairon and Mohammadi, Fatemeh and Montaño, Jonathan}, year={2022} }
@article{chen_cid-ruiz_härkönen_krone_leykin_2022, title={Noetherian operators in Macaulay2}, url={http://dx.doi.org/10.2140/jsag.2022.12.33}, DOI={10.2140/jsag.2022.12.33}, abstractNote={A primary ideal in a polynomial ring can be described by the variety it defines and a finite set of Noetherian operators, which are differential operators with polynomial coefficients. We implement both symbolic and numerical algorithms to produce such a description in various scenarios as well as routines for studying affine schemes through the prism of Noetherian operators and Macaulay dual spaces.}, journal={Journal of Software for Algebra and Geometry}, author={Chen, Justin and Cid-Ruiz, Yairon and Härkönen, Marc and Krone, Robert and Leykin, Anton}, year={2022}, month={Dec} }
@article{cid-ruiz_sturmfels_2023, title={Primary Decomposition with Differential Operators}, url={http://dx.doi.org/10.1093/imrn/rnac178}, DOI={10.1093/imrn/rnac178}, abstractNote={Abstract We introduce differential primary decompositions for ideals in a commutative ring. Ideal membership is characterized by differential conditions. The minimal number of conditions needed is the arithmetic multiplicity. Minimal differential primary decompositions are unique up to change of bases. Our results generalize the construction of Noetherian operators for primary ideals in the analytic theory of Ehrenpreis–Palamodov, and they offer a concise method for representing affine schemes. The case of modules is also addressed. We implemented an algorithm in Macaulay2 that computes the minimal decomposition for an ideal in a polynomial ring.}, journal={International Mathematics Research Notices}, author={Cid-Ruiz, Yairon and Sturmfels, Bernd}, year={2023}, month={Jul} }
@article{chen_cid-ruiz_2022, title={Primary decomposition of modules: A computational differential approach}, url={http://dx.doi.org/10.1016/j.jpaa.2022.107080}, DOI={10.1016/j.jpaa.2022.107080}, journal={Journal of Pure and Applied Algebra}, author={Chen, Justin and Cid-Ruiz, Yairon}, year={2022}, month={Oct} }
@article{equations and multidegrees for inverse symmetric matrix pairs_2021, url={https://doi.org/10.4418/2021.76.2.5}, DOI={10.4418/2021.76.2.5}, journal={Le Matematiche}, year={2021} }
@article{chardin_cid-ruiz_simis_2021, title={Generic freeness of local cohomology and graded specialization}, url={http://dx.doi.org/10.1090/tran/8316}, DOI={10.1090/tran/8316}, abstractNote={The main focus is the generic freeness of local cohomology modules in a graded setting. The present approach takes place in a quite nonrestrictive setting, by solely assuming that the ground coefficient ring is Noetherian. Under additional assumptions, such as when the latter is reduced or a domain, the outcome turns out to be stronger. One important application of these considerations is to the specialization of rational maps and of symmetric and Rees powers of a module.}, journal={Transactions of the American Mathematical Society}, author={Chardin, Marc and Cid-Ruiz, Yairon and Simis, Aron}, year={2021}, month={Oct} }
@article{cid-ruiz_montaño_2022, title={Mixed multiplicities of graded families of ideals}, url={http://dx.doi.org/10.1016/j.jalgebra.2021.10.010}, DOI={10.1016/j.jalgebra.2021.10.010}, journal={Journal of Algebra}, author={Cid-Ruiz, Yairon and Montaño, Jonathan}, year={2022}, month={Jan} }
@article{cid-ruiz_mukundan_2021, title={Multiplicity of the Saturated Special Fiber Ring of Height Three Gorenstein Ideals}, url={http://dx.doi.org/10.1007/s40306-020-00410-1}, DOI={10.1007/s40306-020-00410-1}, journal={Acta Mathematica Vietnamica}, author={Cid-Ruiz, Yairon and Mukundan, Vivek}, year={2021}, month={Dec} }
@article{cid-ruiz_homs_sturmfels_2021, title={Primary Ideals and Their Differential Equations}, url={http://dx.doi.org/10.1007/s10208-020-09485-6}, DOI={10.1007/s10208-020-09485-6}, journal={Foundations of Computational Mathematics}, author={Cid-Ruiz, Yairon and Homs, Roser and Sturmfels, Bernd}, year={2021}, month={Oct} }
@article{cid-ruiz_ramkumar_2021, title={The fiber-full scheme}, journal={arXiv preprint arXiv:2108.13986}, author={Cid-Ruiz, Yairon and Ramkumar, Ritvik}, year={2021} }
@article{castillo_cid-ruiz_li_montaño_zhang_2021, title={When are multidegrees positive?}, volume={85B}, journal={Sém. Lothar. Combin.}, author={Castillo, Federico and Cid-Ruiz, Yairon and Li, Binglin and Montaño, Jonathan and Zhang, Naizhen}, year={2021}, pages={Art. 46, 12} }
@article{busé_cid‐ruiz_d'andrea_2020, title={Degree and birationality of multi‐graded rational maps}, url={http://dx.doi.org/10.1112/plms.12336}, DOI={10.1112/plms.12336}, abstractNote={We give formulas and effective sharp bounds for the degree of multi-graded rational maps and provide some effective and computable criteria for birationality in terms of their algebraic and geometric properties. We also extend the Jacobian dual criterion to the multi-graded setting. Our approach is based on the study of blow-up algebras, including syzygies, of the ideal generated by the defining polynomials of the rational map. A key ingredient is a new algebra that we call the "saturated special fiber ring", which turns out to be a fundamental tool to analyze the degree of a rational map. We also provide a very effective birationality criterion and a complete description of the equations of the associated Rees algebra of a particular class of plane rational maps.}, journal={Proceedings of the London Mathematical Society}, author={Busé, Laurent and Cid‐Ruiz, Yairon and D'Andrea, Carlos}, year={2020}, month={Oct} }
@article{cid-ruiz_simis_2022, title={Degree of Rational Maps and Specialization}, url={http://dx.doi.org/10.1093/imrn/rnaa183}, DOI={10.1093/imrn/rnaa183}, abstractNote={Abstract One considers the behavior of the degree of a rational map under specialization of the coefficients of the defining linear system. The method rests on the classical idea of Kronecker as applied to the context of projective schemes and their specializations. For the theory to work, one is led to develop the details of rational maps and their graphs when the ground ring of coefficients is a Noetherian domain.}, journal={International Mathematics Research Notices}, author={Cid-Ruiz, Yairon and Simis, Aron}, year={2022}, month={Mar} }
@article{cid-ruiz_2021, title={Mixed multiplicities and projective degrees of rational maps}, url={http://dx.doi.org/10.1016/j.jalgebra.2020.08.037}, DOI={10.1016/j.jalgebra.2020.08.037}, journal={Journal of Algebra}, author={Cid-Ruiz, Yairon}, year={2021}, month={Jan} }
@article{cid-ruiz_2021, title={Noetherian operators, primary submodules and symbolic powers}, url={http://dx.doi.org/10.1007/s13348-020-00285-3}, DOI={10.1007/s13348-020-00285-3}, journal={Collectanea Mathematica}, author={Cid-Ruiz, Yairon}, year={2021}, month={Jan} }
@article{castillo_cid-ruiz_li_montaño_zhang_2020, title={When are multidegrees positive?}, url={http://dx.doi.org/10.1016/j.aim.2020.107382}, DOI={10.1016/j.aim.2020.107382}, journal={Advances in Mathematics}, author={Castillo, Federico and Cid-Ruiz, Yairon and Li, Binglin and Montaño, Jonathan and Zhang, Naizhen}, year={2020}, month={Nov} }
@article{cid-ruiz_2019, title={Bounding the degrees of a minimal μ-basis for a rational surface parametrization}, url={http://dx.doi.org/10.1016/j.jsc.2019.02.003}, DOI={10.1016/j.jsc.2019.02.003}, journal={Journal of Symbolic Computation}, author={Cid-Ruiz, Yairon}, year={2019}, month={Nov} }
@article{cid-ruiz_2019, title={Multiplicity of the saturated special fiber ring of height two perfect ideals}, url={http://dx.doi.org/10.1090/proc/14693}, DOI={10.1090/proc/14693}, abstractNote={Let R R be a polynomial ring and let I ⊂ R I \subset R be a perfect ideal of height two minimally generated by forms of the same degree. We provide a formula for the multiplicity of the saturated special fiber ring of I I . Interestingly, this formula is equal to an elementary symmetric polynomial in terms of the degrees of the syzygies of I I . Applying ideas introduced by Busé, D’Andrea, and the author, we obtain the value of the j j -multiplicity of I I and an effective method for determining the degree and birationality of rational maps defined by homogeneous generators of I I .}, journal={Proceedings of the American Mathematical Society}, author={Cid-Ruiz, Yairon}, year={2019}, month={Jul} }
@article{cid-ruiz_jafari_nemati_picone_2020, title={Regularity of bicyclic graphs and their powers}, url={http://dx.doi.org/10.1142/s0219498820500577}, DOI={10.1142/s0219498820500577}, abstractNote={Let [Formula: see text] be the edge ideal of a bicyclic graph [Formula: see text] with a dumbbell as the base graph. In this paper, we characterize the Castelnuovo–Mumford regularity of [Formula: see text] in terms of the induced matching number of [Formula: see text]. For the base case of this family of graphs, i.e. dumbbell graphs, we explicitly compute the induced matching number. Moreover, we prove that [Formula: see text], for all [Formula: see text], when [Formula: see text] is a dumbbell graph with a connecting path having no more than two vertices.}, journal={Journal of Algebra and Its Applications}, author={Cid-Ruiz, Yairon and Jafari, Sepehr and Nemati, Navid and Picone, Beatrice}, year={2020}, month={Mar} }
@article{regularity and gröbner bases of the rees algebra of edge ideals of bipartite graphs_2018, url={https://doi.org/10.4418/2018.73.2.4}, DOI={10.4418/2018.73.2.4}, abstractNote={Let $G$ be a bipartite graph and $I=I(G)$ be its edge ideal. Let $G$ be a bipartite graph and $I=I(G)$ be its edge ideal. The aim of this note is to investigate different aspects of the Rees algebra $\Rees(I)$ of $I$. We compute its regularity and the universal Gr\obner basis of its defining equations; interestingly, both of them are described in terms of the combinatorics of $G$.
We apply these ideas to study the regularity of the powers of $I$. For any $s \ge \text{match}(G)+\lvert E(G) \rvert +1$ we prove that $\reg(I^{s+1})=\reg(I^s)+2$ and that for an $s\ge 1$ we have the inequality $\reg(I^s) \le 2s + \MM(G) - 1$.}, journal={Le Matematiche}, year={2018} }