Roberto Muñoz
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Roberto Muñoz has a total of 17 co-authors. Here are the top co-authors by number of shared publications:
- Luis Eduardo Sola Conde
Dipartimento di Matematica, Università degli Studi di Trento, Trento, Italy
21 shared publications - Gianluca Occhetta
Dipartimento di Matematica, Università degli Studi di Trento, Trento, Italy
17 shared publications - Angelo Felice Lopez
Dipartimento di Matematica e Fisica, Università di Roma Tre, Rome, Italy
10 shared publications - José Carlos Sierra
Instituto de Ciencias Matemáticas (ICMAT), Consejo Superior de Investigaciones Científicas (CSIC), Campus de Cantoblanco, 28049 Madrid, Spain
7 shared publications - Antonio Lanteri
Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, Milan, Italy
5 shared publications - Kiwamu Watanabe
Department of Mathematics, Faculty of Science and Engineering, Chuo University, Tokyo, Japan
2 shared publications
Latest Publications
- Open Access
- 1 October 2024
- Published by Modestum Ltd in International Electronic Journal of Mathematics Education
- Vol. 19 (4) , em0789
Elementary mathematics teacher education programs in Greece, Romania, and Spain
As a contribution to the discussion of how to improve the initial teacher training in mathematics of elementary teachers, this work presents a descriptive and comparative study of the courses devoted to mathematics and mathematics education in the education degrees of Greek, Romanian, and Spanish universities. Considering the constrains of each national law and within the Mathematics Teacher’s Specialized Knowledge model framework, we analyze the official descriptions of such courses to organize them by their content, to describe their distribution along each degree, and to study the optional and specialization courses in mathematics offered by each university. Data are compared among countries, and across programs within each country, with the aim of including similar studies from other states. Moreover, they are confronted with the National Council on Teacher Quality standards for the mathematics preparation of elementary teachers, showing that, in general lines, GRS data seem not to be in tune with such standards.
- 1 October 2024
- Published by Modestum Ltd in International Electronic Journal of Mathematics Education
- Vol. 19 (4) , em0789
Open AccessElementary mathematics teacher education programs in Greece, Romania, and Spain
As a contribution to the discussion of how to improve the initial teacher training in mathematics of elementary teachers, this work presents a descriptive and comparative study of the courses devoted to mathematics and mathematics education in the education degrees of Greek, Romanian, and Spanish universities. Considering the constrains of each national law and within the Mathematics Teacher’s Specialized Knowledge model framework, we analyze the official descriptions of such courses to organize them by their content, to describe their distribution along each degree, and to study the optional and specialization courses in mathematics offered by each university. Data are compared among countries, and across programs within each country, with the aim of including similar studies from other states. Moreover, they are confronted with the National Council on Teacher Quality standards for the mathematics preparation of elementary teachers, showing that, in general lines, GRS data seem not to be in tune with such standards.
- Open Access
On the classification of non-big Ulrich vector bundles on fourfolds
We give an almost complete classification of non-big Ulrich vector bundles on fourfolds. This allows to classify them in the case of Picard rank one fourfolds, of Mukai fourfolds and in the case of Del Pezzo $n$-folds for $n \le 4$. We also classify Ulrich bundles with non-big determinant on Del Pezzo and Mukai $n$-folds, $n \ge 2$.Open AccessOn the classification of non-big Ulrich vector bundles on fourfolds
We give an almost complete classification of non-big Ulrich vector bundles on fourfolds. This allows to classify them in the case of Picard rank one fourfolds, of Mukai fourfolds and in the case of Del Pezzo $n$-folds for $n \le 4$. We also classify Ulrich bundles with non-big determinant on Del Pezzo and Mukai $n$-folds, $n \ge 2$. - Open Access
- 5 September 2023
- Published by Springer Nature in manuscripta mathematica
- Vol. 174 (1-2) , 517-533
Non-big Ulrich bundles: the classification on quadrics and the case of small numerical dimension
On any smooth n-dimensional variety we give a pretty precise picture of rank r Ulrich vector bundles with numerical dimension at most $$\frac{n}{2}+r-1$$ . Also, we classify non-big Ulrich vector bundles on quadrics and on the Del Pezzo fourfold of degree 6.- 5 September 2023
- Published by Springer Nature in manuscripta mathematica
- Vol. 174 (1-2) , 517-533
Open AccessNon-big Ulrich bundles: the classification on quadrics and the case of small numerical dimension
On any smooth n-dimensional variety we give a pretty precise picture of rank r Ulrich vector bundles with numerical dimension at most $$\frac{n}{2}+r-1$$ . Also, we classify non-big Ulrich vector bundles on quadrics and on the Del Pezzo fourfold of degree 6. - Open Access
Non-big Ulrich bundles: the classification on quadrics and the case of small numerical dimension
On any smooth $n$-dimensional variety we give a pretty precise picture of rank $r$ Ulrich vector bundles with numerical dimension at most $\frac{n}{2}+r-1$. Also, we classify non-big Ulrich vector bundles on quadrics and on the Del Pezzo fourfold of degree $6$.Open AccessNon-big Ulrich bundles: the classification on quadrics and the case of small numerical dimension
On any smooth $n$-dimensional variety we give a pretty precise picture of rank $r$ Ulrich vector bundles with numerical dimension at most $\frac{n}{2}+r-1$. Also, we classify non-big Ulrich vector bundles on quadrics and on the Del Pezzo fourfold of degree $6$. - Open Access
Maximal disjoint Schubert cycles in rational homogeneous varieties
In this paper we study properties of the Chow ring of rational homogeneous varieties of classical type, more concretely, effective zero divisors of low codimension, and a related invariant called effective good divisibility. This information is then used to study the question of (non)existence of nonconstant maps among these varieties, generalizing previous results for projective spaces and Grassmannians.
Open AccessMaximal disjoint Schubert cycles in rational homogeneous varieties
In this paper we study properties of the Chow ring of rational homogeneous varieties of classical type, more concretely, effective zero divisors of low codimension, and a related invariant called effective good divisibility. This information is then used to study the question of (non)existence of nonconstant maps among these varieties, generalizing previous results for projective spaces and Grassmannians.
- 1 March 2022
- Published by Springer Nature in Transformation Groups
- Vol. 27 (1) , 189-223
NESTINGS OF RATIONAL HOMOGENEOUS VARIETIES
- 1 March 2022
- Published by Springer Nature in Transformation Groups
- Vol. 27 (1) , 189-223
NESTINGS OF RATIONAL HOMOGENEOUS VARIETIES
- 21 June 2021
- Published by Taylor & Francis in Communications in Algebra
- Vol. 49 (12) , 5109-5128
Discriminants of toric varieties
We study the subvariety of singular sections, the discriminant, of a base point free linear system on a smooth toric variety X. On one hand we describe pairs (X, L) for which the discriminant is of low dimension. Precisely, we collect some bounds on this dimension and classify those pairs whose dimension differs the bound less than or equal to two. On the other hand we study the degree of the discriminant for some relevant families on polarized toric varieties, describing their minimal values and the region of the ample cone where this minimal is attained.- 21 June 2021
- Published by Taylor & Francis in Communications in Algebra
- Vol. 49 (12) , 5109-5128
Discriminants of toric varieties
We study the subvariety of singular sections, the discriminant, of a base point free linear system on a smooth toric variety X. On one hand we describe pairs (X, L) for which the discriminant is of low dimension. Precisely, we collect some bounds on this dimension and classify those pairs whose dimension differs the bound less than or equal to two. On the other hand we study the degree of the discriminant for some relevant families on polarized toric varieties, describing their minimal values and the region of the ample cone where this minimal is attained.- Open Access
Discriminants of Toric Varieties
We study the subvariety of singular sections, the discriminant, of a base point free linear system $|L|$ on a smooth toric variety $X$. On one hand we describe pairs $(X,L)$ for which the discriminant is of low dimension. Precisely, we collect some bounds on this dimension and classify those pairs whose dimension differs the bound less than or equal to two. On the other hand we study the degree of the discriminant for some relevant families on polarized toric varieties, describing their minimal values and the region of the ample cone where this minimal is attained.Open AccessDiscriminants of Toric Varieties
We study the subvariety of singular sections, the discriminant, of a base point free linear system $|L|$ on a smooth toric variety $X$. On one hand we describe pairs $(X,L)$ for which the discriminant is of low dimension. Precisely, we collect some bounds on this dimension and classify those pairs whose dimension differs the bound less than or equal to two. On the other hand we study the degree of the discriminant for some relevant families on polarized toric varieties, describing their minimal values and the region of the ample cone where this minimal is attained. - Open Access
On the classification of non-big Ulrich vector bundles on surfaces and threefolds
We classify Ulrich vector bundles that are not big on smooth complex surfaces and threefolds.
Open AccessOn the classification of non-big Ulrich vector bundles on surfaces and threefolds
We classify Ulrich vector bundles that are not big on smooth complex surfaces and threefolds.
- Open Access
Nestings of rational homogeneous varieties
In this paper we study the existence of sections of universal bundles on rational homogeneous varieties -- called nestings -- classifying them completely in the case in which the Lie algebra of the automorphism group of the variety is simple of classical type. In particular we show that, under this hypothesis, nestings do not exist unless there exists a proper algebraic subgroup of the automorphism group acting transitively on the base variety.
Open AccessNestings of rational homogeneous varieties
In this paper we study the existence of sections of universal bundles on rational homogeneous varieties -- called nestings -- classifying them completely in the case in which the Lie algebra of the automorphism group of the variety is simple of classical type. In particular we show that, under this hypothesis, nestings do not exist unless there exists a proper algebraic subgroup of the automorphism group acting transitively on the base variety.