Fourier-Mukai transforms for coherent systems on elliptic curves

We determine all the Fourier-Mukai transforms for coherent systems consisting of a vector bundle over an elliptic curve and a subspace of its global sections, showing that these transforms are indexed by the positive integers. We prove that the natural stability condition for coherent systems, which depends on a parameter, is preserved by these transforms for small and large values of the parameter. By means of the Fourier-Mukai transforms we prove that certain moduli spaces of coherent systems corresponding to small and large values of the parameter are isomorphic. Using these results we draw some conclusions about the possible birational type of the moduli spaces. We prove that for a given degree $d$ of the vector bundle and a given dimension of the subspace of its global sections there are at most $d$ different possible birational types for the moduli spaces.Comment: LaTeX2e, 21 pages, some proofs simplified, typos corrected. Final version to appear in Journal of the London Mathematical Societ

Aproximación histórica al origen del ius postliminíi

Sin resume

Moduli Spaces of Semistable Sheaves on Singular Genus One Curves

We find some equivalences of the derived category of coherent sheaves on a Gorenstein genus one curve that preserve the (semi)-stability of pure dimensional sheaves. Using them we establish new identifications between certain Simpson moduli spaces of semistable sheaves on the curve. For rank zero, the moduli spaces are symmetric powers of the curve whilst for a fixed positive rank there are only a finite number of non-isomorphic spaces. We prove similar results for the relative semistable moduli spaces on an arbitrary genus one fibration with no conditions either on the base or on the total space. For a cycle $E_N$ of projective lines, we show that the unique degree 0 stable sheaves are the line bundles having degree 0 on every irreducible component and the sheaves $\mathcal{O}(-1)$ supported on one irreducible component. We also prove that the connected component of the moduli space that contains vector bundles of rank $r$ is isomorphic to the $r$-th symmetric product of the rational curve with one node.Comment: 26 pages, 4 figures. Added the structure of the biggest component of the moduli space of sheaves of degree 0 on a cycle of projective lines. Final version; to appear en IMRS (International Mathematics Research Notices 2009

Percentiles of sums of heavy-tailed random variables: Beyond the single-loss approximation

The final publication is available at Springer via http://dx.doi.org/10.1007/s11222-013-9376-6A perturbative approach is used to derive approximations of arbitrary order to estimate high percentiles of sums of positive independent random variables that exhibit heavy tails. Closed-form expressions for the successive approximations are obtained both when the number of terms in the sum is deterministic and when it is random. The zeroth order approximation is the percentile of the maximum term in the sum. Higher orders in the perturbative series involve the right-truncated moments of the individual random variables that appear in the sum. These censored moments are always finite. As a result, and in contrast to previous approximations proposed in the literature, the perturbative series has the same form regardless of whether these random variables have a finite mean or not. For high percentiles, and specially for heavier tails, the quality of the estimate improves as more terms are included in the series, up to a certain order. Beyond that order the convergence of the series deteriorates. Nevertheless, the approximations obtained by truncating the perturbative series at intermediate orders are remarkably accurate for a variety of distributions in a wide range of parameters.The authors thank the anonymous reviewers for their valuable comments and suggestions. A.S. acknowledges financial support from the Spanish Dirección General de Investigación, project TIN2010-21575-C02-02

Las asociaciones profesionales en Derecho Romano

Se estudia fundamentalmente la evolución histórica del régimen asociativo romano, desde los primitivos colegios que se sitúan en la época monárquica y que aparecen participando, aunque no con carácter corporativo en el ejército Serviano, hasta los colegios obligatorios del Bajo Imperio. Pasando por el analisis del precepto de las XII tablas en que se protege la libertad de pactos de los asociados. El Senado consulto de las Bacanales, las medidas adoptadas en los años 64 y 56 a. de C., la ley Licinia, las disposiciones establecidas contra la corrupción electoral y las leyes de Cesar y Augusto sobre los colegios; también se dedica especial atención a los Collegia Terniorum

El ritual de Onquesto (Himno Homérico a Apolo, v. 229-238) - The Ritual of Onchestus (Homeric Hymn to Apollo, v. 229-238)

Este trabajo analiza diez versos del Himno Homérico a Apolo (v.229-238), en los que un auriga que conduce un carro tirado por un potro, salta y esperan a ver cómo se estrella el carro. Después hay una oración al dios Posidón. Estudiaré los elementos claves: el Himno Homérico a Apolo y Onquesto, la ciudad de Beocia donde transcurre la acción: desarrollaré someramente su origen micénico y su posible entorno ritual; el dios Posidón, centrándome en su faceta de Hipio, relacionado con los caballos y los carros. Por último, mencionaré el empleo en Grecia del caballo como animal de tiro y el uso del carro. Más tarde ahondaré en la gramática y sintaxis de este fragmento. Procuraré rebatir o defender las aportaciones de los comentaristas de los Himnos, sobre todo las teorías más recientes: las de Roux, Schachter y Teffeteller. Expondré una propuesta de interpretación del texto en la que se baraja la posibilidad de que nos encontremos ante lo que podría ser un ritual. Como refuerzo de esta propuesta, incluyo otros textos que se pueden poner en relación en parte con el suceso tratado, como el ritual de Taraxipo en Olimpia. / This work is an analysis of ten verses from the Homeric Hymn to Apollo (v. 229-238), where a charioteer drives a chariot pulled by a colt and then he jumps, waiting to see how the chariot crashes. After that, there’s a pray for the god Poseidon. I will study the essencial elements: The Homeric Hymn to Apollo and Onchestus, the city in Boeotia where the action takes place, her mycenaean origin and her possible ritual environment; and about the god Poseidon, I will focus on his Hippios version, related with both horses and chariots. Moveover, I will also mention the use of a horse as a draught animal and the utilization of chariots in Ancient Greece. Lately, I delve into the grammar and syntax of this fragment and I will try to refute or concure the critics of the Homeric Hymns, specially referred to the latest theories: those from Roux, Schachter and Teffeteller. Finally I will suggest an interpretation for those verses, where the action might be related to a ritual. According to my interpretation, I will also include some texts that can be associated with the main issue, such as the ritual to Taraxippus in Olimpia