The bogomolov conjecture for totally degenerate Abelian varieties

We prove the Bogomolov conjecture for a totally degenerate abelian variety A over a function field. We adapt Zhang's proof of the number field case replacing the complex analytic tools by tropical analytic geometry. A key step is the tropical equidistribution theorem for A at the totally degenerate place.

Tropical varieties for non-archimedean analytic spaces

"Vegeu el resum a l'inici del document del fitxer adjunt."

Diophantine approximation on projective varieties I: algebraic distance and metric Bézout theorem

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Strong exceptional sequences of vector bundles on certain Fano varieties

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Evaluation of susceptibility of pear and plum varieties and rootstocks to Ca. P. pyri and Ca. P. prunorum using Real-Time PCR

Real-time PCR was used to quantify phytoplasma concentration in fifty inoculated trees from five Prunus rootstocks and in forty-eight symptomatic pear and Japanese plum trees from orchards. Seasonal fluctuation of Ca. P. prunorum in different Prunus rootstocks, over three years, showed that the highest percentage detected by nested-PCR was in the ‘Garnem’ rootstock on nearly all sampling dates. Intra-varietal differences were also observed. Phytoplasma titer could be estimated by real time PCR in some trees of the rootstocks ‘Garnem’, ‘Barrier’, ‘GF-677’ and ‘Marianna’, and ranged from 4.7x105 to 3.18x109 phytoplasmas per gram of tissue. Quantification by real-time PCR was not possible in the ‘Cadaman’ trees analyzed, probably due to a lower phytoplasma titer in this variety. Samples from infected trees from commercial plots had different phytoplasma concentration and detection percentage depending on the variety, both being lower in ‘Fortune’ and ‘606’ Japanese plum and in ‘Blanquilla’ pear trees.

The varieties of regional change

Many metropolitan areas have experienced extreme boom-bust cycles over the past century. Some places, like Detroit, grew enormously as industrial powerhouses and then declined, while other older cities, like Boston, seem quite resilient. Education does a reasonable job of explaining urban resilience. In this paper, we present a simple model where education increases the level of entrepreneurship. In this model, human capital spillovers occur at the city level because skilled workers produce more product varieties and thereby increase labor demand. We decompose empirically the causes of the connection between skills and urban success and find that skills are associated with growth in productivity or entrepreneurship, not with growth in quality of life, at least outside of the West. We also find that skills seem to have depressed housing supply growth in the West, but not in other regions, which supports the view that educated residents in that region have fought for tougher land-use controls. We also present evidence that skills have had a disproportionately large impact on unemployment during the current recession.

The Brauer group and the second Abel-Jacobi map for 0-cycles on algebraic varieties

This paper focuses on the connection between the Brauer group and the 0-cycles of an algebraic variety. We give an alternative construction of the second l-adic Abel-Jacobi map for such cycles, linked to the algebraic geometry of Severi-Brauer varieties on X. This allows us then to relate this Abel-Jacobi map to the standard pairing between 0-cycles and Brauer groups (see [M], [L]), completing results from [M] in this direction. Second, for surfaces, it allows us to present this map according to the more geometrical approach devised by M. Green in the framework of (arithmetic) mixed Hodge structures (see [G]). Needless to say, this paper owes much to the work of U. Jannsen and, especially, to his recently published older letter [J4] to B. Gross.

Arithmetical problems in number fields, abelian varieties and modular forms

Number theory, a fascinating area in mathematics and one of the oldest, has experienced spectacular progress in recent years. The development of a deep theoretical background and the implementation of algorithms have led to new and interesting interrelations with mathematics in general which have paved the way for the emergence of major theorems in the area. This report summarizes the contribution to number theory made by the members of the Seminari de Teoria de Nombres (UB-UAB-UPC) in Barcelona. These results are presented in connection with the state of certain arithmetical problems, and so this monograph seeks to provide readers with a glimpse of some specific lines of current mathematical research.

Athermal character of structural phase transitions

The significance of thermal fluctuations in nucleation in structural first-order phase transitions has been examined. The prototypical case of martensitic transitions has been experimentally investigated by means of acoustic emission techniques. We propose a model based on the mean first-passage time to account for the experimental observations. Our study provides a unified framework to establish the conditions for isothermal and athermal transitions to be observed.

Local character of magnetic coupling in ionic solids

Magnetic interactions in ionic solids are studied using parameter-free methods designed to provide accurate energy differences associated with quantum states defining the Heisenberg constant J. For a series of ionic solids including KNiF3, K2NiF4, KCuF3, K2CuF4, and high- Tc parent compound La2CuO4, the J experimental value is quantitatively reproduced. This result has fundamental implications because J values have been calculated from a finite cluster model whereas experiments refer to infinite solids. The present study permits us to firmly establish that in these wide-gap insulators, J is determined from strongly local electronic interactions involving two magnetic centers only thus providing an ab initio support to commonly used model Hamiltonians.

Velar verbs and verbal classes in catalan

There is in Catalan a set of verbs, the so-called «velar verbs», whose differential characteristic consists in presenting a velar segment between the root and the inflectional suffixes in certain morphosyntactic contexts. This velar segment has traditionally been considered as being part of the root in the contexts where it occurs, and has been made responsible for the typical allomorphic character of velar verbs. Under the assumption that regular verbs are only one-root verbs, velar verbs have been treated as irregular verbs. Nevertheless, neither the phonic character of the velar segment nor the marginal character of velar verbs is clear. The aim of this paper is to present a different account of velar verbs on the basis of the inflectional morphological character of the velar segment. The work is split into two parts. The first one focuses on standard Catalan, and tries to show that in this variety velar verbs are better treated as regular verbs. The second one focuses on other Catalan varieties, and aims to exhibit the incoherence implied in the traditional treatment of velar verbs in the context of the Catalan language as a whole. The discussion is mainly developed on morphological grounds, halfway between theory and description.

On the bicanonical map of irregular varieties

From the point of view of uniform bounds for the birationality of pluricanonical maps, irregular varieties of general type and maximal Albanese dimension behave similarly to curves. In fact Chen-Hacon showed that, at least when their holomorphic Euler characteristic is positive, the tricanonical map of such varieties is always birational. In this paper we study the bicanonical map. We consider the natural subclass of varieties of maximal Albanese dimension formed by primitive varieties of Albanese general type. We prove that the only such varieties with non-birational bicanonical map are the natural higher-dimensional generalization to this context of curves of genus $2$: varieties birationally equivalent to the theta-divisor of an indecomposable principally polarized abelian variety. The proof is based on the (generalized) Fourier-Mukai transform.

Post-market environmental monitoring of Bt maize in Spain: Non-target effects of varieties derived from the event MON810 on predatory fauna

The Spanish Government has established post-market environmental monitoring (PMEM) as mandatory for genetically modified (GM) crop varieties cultivated in Spain. In order to comply with this regulation, effects of Bt maize varieties derived from the event MON810 on the predatory fauna were monitored for two years in northeast and central Spain. The study was carried out with a randomized block design in maize fields of 3-4 ha on which the abundance of plant-dwelling predators and the activity-density of soil-dwelling predators in Bt vs. non-Bt near-isogenic varieties were compared. To this end, the plots were sampled by visual inspection of a certain number of plants and pitfall traps 6 or 7 times throughout two seasons. No significant differences in predator densities on plants were found between Bt and non-Bt varieties. In the pitfall traps, significant differences between the two types of maize were found only in Staphylinidae, in which trap catches in non-Bt maize were higher than in Bt maize in central Spain. Based on the statistical power of the assays, surrogate arthropods for PMEM purposes are proposed; Orius spp. and Araneae for visual sampling and Carabidae, Araneae, and Staphylinidae for pitfall trapping. The other predator groups recorded in the study, Nabis sp. and Coccinellidae in visual sampling and Dermaptera in pitfall trapping, gave very poor power results. To help to establish a standardized protocol for PMEM of genetically modified crops, the effect-detecting capacity with a power of 0.8 of each predator group is given.

The Impact of a Character Posture Model on the Communication of Affect in an Immersive Virtual Environment

This paper presents the quantitative and qualitative findings from an experiment designed to evaluate a developing model of affective postures for full-body virtual characters in immersive virtual environments (IVEs). Forty-nine participants were each requested to explore a virtual environment by asking two virtual characters for instructions. The participants used a CAVE-like system to explore the environment. Participant responses and their impression of the virtual characters were evaluated through a wide variety of both quantitative and qualitative methods. Combining a controlled experimental approach with various data-collection methods provided a number of advantages such as providing a reason to the quantitative results. The quantitative results indicate that posture plays an important role in the communication of affect by virtual characters. The qualitative findings indicated that participants attribute a variety of psychological states to the behavioral cues displayed by virtual characters. In addition, participants tended to interpret the social context portrayed by the virtual characters in a holistic manner. This suggests that one aspect of the virtual scene colors the perception of the whole social context portrayed by the virtual characters. We conclude by discussing the importance of designing holistically congruent virtual characters especially in immersive settings.