arXiv subjects
Publications and source records attributed to Roberto Muñoz.
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, $n \ge 2$.
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 $6$.
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.
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.
We classify Ulrich vector bundles that are not big on smooth complex surfaces and threefolds.
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.
As a natural extension of the theory of uniform vector bundles on Fano manifolds, we consider uniform principal bundles, and study them by means of the associated flag bundles, as their natural projective geometric realizations. In this paper we develop the necessary background, and prove some theorems that are flag bundle counterparts of some of the central results in the theory of uniform vector bundles.
We present here some conjectures on the diagonalizability of uniform principal bundles on rational homogeneous spaces, that are natural extensions of classical theorems on uniform vector bundles on the projective space, and study the validity of these conjectures in the case of classical groups.
We present an analysis of 39 nuclei and their early-type hosts in the Virgo Cluster using ten broadband filters: F300W, F475W, F850LP, F160W, $u^*griz$, and $K_s$. We describe the Virgo Redux program, which provides high-resolution UV and NIR imaging. Combining this data with optical and NIR imaging from the ACS Virgo Cluster Survey and the Next Generation Virgo Cluster Survey, we estimate masses, metallicities and ages using simple stellar population (SSP) models. For 19 nuclei, we compare to SSP parameters derived from Keck and Gemini spectra and find reasonable agreement between the photometric and spectroscopic metallicity: the RMS scatter is 0.3 dex. We reproduce the nucleus-galaxy mass fraction of $0.33^{+0.09}_{-0.07}$ percent for galaxy stellar masses $10^{8.4}-10^{10.3} M_\odot$ with a typical precision of $\sim$35% for the nuclei masses. Based on available model predictions, there is no single preferred formation scenario for nuclei, suggesting that nuclei are formed stochastically through a mix of processes. Nuclei metallicities are statistically identical to those of their hosts, appearing $0.07 \pm 0.3$ dex more metal-rich on average -- although, omitting galaxies with unusual origins, nuclei are $0.20\pm0.28$ dex more metal-rich. Nuclei appear to be $0.56 \pm 0.12$ dex more metal rich than ultra-compact dwarf galaxies (UCDs) at fixed mass. We find no clear age difference between nuclei and their galaxies, with nuclei displaying a broad range of ages. Interestingly, we find that the most massive nuclei may be flatter and more closely aligned with the semi-major axes of their hosts, suggesting that they formed through predominantly dissipative processes.
In 1991 Campana and Peternell proposed, as a natural algebro-geometric extension of Mori's characterization of the projective space, the problem of classifying the complex projective Fano manifolds whose tangent bundle is nef, conjecturing that the only varieties satisfying these properties are rational homogeneous. In this paper we review some background material related to this problem, with special attention to the partial results recently obtained by the authors.
A Fano manifold $X$ with nef tangent bundle is of flag-type if it has the same type of elementary contractions as a complete flag manifold. In this paper we present a method to associate a Dynkin diagram $\mathcal{D}(X)$ with any such $X$, based on the numerical properties of its contractions. We then show that $\mathcal{D}(X)$ is the Dynkin diagram of a semisimple Lie group. As an application we prove that Campana-Peternell conjecture holds when $X$ is a flag-type manifold whose Dynkin diagram is $A_n$ ($X$ is shown to be the complete flag in $\mathbb{P}^n$).
In this work we deal with vector bundles of rank two on a Fano manifold $X$ with $b_2=b_4=1$. We study the nef and pseudoeffective cones of the corresponding projectivizations and how these cones are related to the decomposability of the vector bundle. As consequences, we obtain the complete list of $\mathbb{P}^1$-bundles over $X$ that have a second $\mathbb{P}^1$-bundle structure, classify all the uniform rank two vector bundles on this class of Fano manifolds and show the stability of indecomposable Fano bundles (with one exception on $\mathbb{P}^2$).
In this paper we classify rank two Fano bundles $\cE$ on Fano manifolds satisfying $H^2(X,\Z)\cong H^4(X,\Z)\cong\Z$. The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization ${\mathbb{P}}(\cE)$, that allows us to obtain the cohomological invariants of $X$ and $\cE$. As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.
We present the discovery of an extremely bright and extended lensed source from the second Red Sequence Cluster Survey (RCS2). RCSGA 032727-132609 is spectroscopically confirmed as a giant arc and counter-image of a background galaxy at $z=1.701$, strongly-lensed by the foreground galaxy cluster RCS2 032727-132623 at $z=0.564$. The giant arc extends over $\sim 38$\,\arcsec and has an integrated $g$-band magnitude of 19.15, making it $\sim 20$ times larger and $\sim 4$ times brighter than the prototypical lensed galaxy MS1512-cB58. This is the brightest distant lensed galaxy in the Universe known to date. Its location in the `redshift desert' provides unique opportunities to connect between the large samples of galaxies known at $z\sim3$ and $z\sim1$. We have collected photometry in 9 bands, ranging from $u$ to $K_s$, which densely sample the rest-frame UV and optical light, including the age-sensitive 4000Å break. A lens model is constructed for the system, and results in a robust total magnification of $2.04 \pm 0.16$ for the counter-image; we estimate an average magnification of $17.2 \pm 1.4$ for the giant arc based on the relative physical scales of the arc and counter-image. Fits of single-component spectral energy distribution (SED) models to the photometry result in a moderately young age, $t = 115 \pm 65$\,Myr, small amounts of dust, $E(B-V) \le 0.035$, and an exponentially declining star formation history with \textit{e}-folding time $τ= 10-100$\,Myr. After correcting for the lensing magnification, we find a stellar mass of $\log(\mathrm{M}/\mathrm{M}_\odot)=10.0 \pm 0.1$. Allowing for episodic star formation, an underlying old burst could contain up to twice the mass inferred from single-component modeling. This stellar mass estimate is consistent with the average stellar mass of a sample of `BM' galaxies ($1.4 < z < 2.0$) studied by Reddy et al. (2006).
Virtual Worlds (VWs) are an emerging technology used by a growing number of educational institutions around the world. It is an environment, a way of learning and an educational tool that allows different levels of online interaction. In the course "Programming I", of the career Informatics Engineering at Universidad de Valparaíso, we conducted a pilot experience with the VW of Second Life, in order to evaluate the potential of using VWs in the teaching practice.
We classify rank two Fano bundles over the Grassmannian of lines $\G(1,4)$. In particular we show that the only non-split rank two Fano bundle over $\G(1,4)$ is, up to a twist, the universal quotient bundle $\cQ$. This completes the classification of rank two Fano bundles over Grassmannians of lines.