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

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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 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.

Theta-duality on Prym varieties and a Torelli Theorem

Let $\pi : \widetilde C \to C$ be an unramified double covering of irreducible smooth curves and let $P$ be the attached Prym variety. We prove the scheme-theoretic theta-dual equalities in the Prym variety $T(\widetilde C)=V^2$ and $T(V^2)=\widetilde C$, where $V^2$ is the Brill-Noether locus of $P$ associated to $\pi$ considered by Welters. As an application we prove a Torelli theorem analogous to the fact that the symmetric product $D^{(g)}$ of a curve $D$ of genus $g$ determines the curve.

Trade liberalization, competition and growth

Increasing evidence support the claim that international trade enhances innovation and productivity growth through an increase in competition. This paper develops a two-country endogenous growth model, with firm specific R&D and a continuum of oligopolistic sectors under Cournot competition to provide a theoretical support to this claim. Since countries are assumed to produce the same set of varieties, trade openness makes markets more competitive, reducing prices and increasing quantities. Under Cournot competition, trade is pro-competitive. Since firms undertake cost reducing innovations, the increase in production induced by a more competitive market push firms to innovate more. Consequently, a reduction on trade barriers enhances growth by reducing domestic firm's market power.

A New open economy macroeconomic model with endogenous portfolio diversification and firms entry

This paper provides a new benchmark for the analysis of the international diversi…cation puzzle in a tractable new open economy macroeconomic model. Building on Cole and Obstfeld (1991) and Heathcote and Perri (2009), this model speci…es an equilibrium model of perfect risk sharing in incomplete markets, with endogenous portfolios and number of varieties. Equity home bias may not be a puzzle but a perfectly optimal allocation for hedging risk. In contrast to previous work, the model shows that: (i) optimal international portfolio diversi…cation is driven by home bias in capital goods, independently of home bias in consumption, and by the share of income accruing to labour. The model explains reasonably well the recent patterns of portfolio allocations in developed economies; and (ii) optimal portfolio shares are independent of market dynamics.

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.

Schooling supply and the structure of production: Evidence from US States 1950-1990

We find that over the period 1950-1990, US states absorbed increases in the supplyof schooling due to tighter compulsory schooling and child labor laws mostly throughwithin-industry increases in the schooling intensity of production. Shifts in the industrycomposition towards more schooling-intensive industries played a less important role.To try and understand this finding theoretically, we consider a free trade model withtwo goods/industries, two skill types, and many regions that produce a fixed rangeof differentiated varieties of the same goods. We find that a calibrated version ofthe model can account for shifts in schooling supply being mostly absorbed throughwithin-industry increases in the schooling intensity of production even if the elasticityof substitution between varieties is substantially higher than estimates in the literature.

Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight 2. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and we study Faltings heights of arithmetic Hirzebruch-Zagier divisors.

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.

Comparison of flag leaf and ear photosynthesis with biomass and grain yield of durum wheat under various water conditions and genotypes

Photosynthetic activity of cereals has traditionally been studied using leaves, thus neglecting the role of other organs such as ears. Here, we studied the effects of water status and genotypes on the photosynthetic activity of the flag leaf blade and the ear of durum wheat. The various parameters related to the photosynthetic activity were analysed in relation to the total above-ground plant biomass and grain yield at maturity. Four local varieties plus two cultivars adapted to the semiarid areas of South Morocco were grown in pots in a greenhouse. Five different water treatments were maintained from the beginning of stem elongation to maturity, when shoot biomass and grain yield were recorded. The net photosynthesis (A), stomatal conductance (gs) and transpiration (T) of the ear and the flag leaf were measured at anthesis. In both organs these factors decreased significantly with water deficit, whereas the A/T and A/gs ratios increased. The genotype effect was also significant for all traits studied. Whole-organ photosynthesis was much higher in the ear than in the flag leaf in well-watered conditions. As water stress developed, photosynthesis decreased less in the ear than in the flag leaf. Whole-ear photosynthesis correlated better than flag leaf photosynthesis with biomass and yield. Nevertheless, the relationships of the whole flag leaf with biomass and yield improved as the water stress became more severe, suggesting a progressive shift of yield from sink to source limitation. For all water regimes the ratios A/gs and A/T of the ear also showed a higher (negative) correlation with both biomass and yield than those of the flag leaf. The results indicate that the ear has a greater photosynthetic role than the flag leaf in determining grain yield, not only in drought but also in the absence of stress.

Cities, skills, and regional change

One approach to urban areas emphasizes the existence of certain immutable relationships, such as Zipf's or Gibrat's Law. An alternative view is that urban changereflects individual responses to changing tastes or technologies. This paper examinesalmost 200 years of regional change in the U.S. and finds that few, if any, growth relationships remain constant, including Gibrat's Law. Education does a reasonable jobof explaining urban resilience in recent decades, but does not seem to predict countygrowth a century ago. After reviewing this evidence, we present and estimate a simple model of regional change, where education increases the level of entrepreneurship.Human capital spillovers occur at the city level because skilled workers produce moreproduct varieties and thereby increase labor demand. We find that skills are associatedwith growth in productivity or entrepreneurship, not with growth in quality of life, atleast outside of the West. We also find that skills seem to have depressed housing supplygrowth in the West, but not in other regions, which supports the view that educatedresidents in that region have fought for tougher land-use controls. We also present evidence that skills have had a disproportionately large impact on unemployment duringthe current recession.

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.

Input diffusion and the evolution of production networks

What determines which inputs are initially considered and eventually adopted in the productionof new or improved goods? Why are some inputs much more prominent than others? We modelthe evolution of input linkages as a process where new producers first search for potentially usefulinputs and then decide which ones to adopt. A new product initially draws a set of 'essentialsuppliers'. The search stage is then confined to the network neighborhood of the latter, i.e., to theinputs used by the essential suppliers. The adoption decision is driven by a tradeoff between thebenefits accruing from input variety and the costs of input adoption. This has important implicationsfor the number of forward linkages that a product (input variety) develops over time. Inputdiffusion is fostered by network centrality ? an input that is initially represented in many networkneighborhoods is subsequently more likely to be adopted. This mechanism also delivers a powerlaw distribution of forward linkages. Our predictions continue to hold when varieties are aggregatedinto sectors. We can thus test them, using detailed sectoral US input-output tables. We showthat initial network proximity of a sector in 1967 significantly increases the likelihood of adoptionthroughout the subsequent four decades. The same is true for rapid productivity growth in aninput-producing sector. Our empirical results highlight two conditions for new products to becomecentral nodes: initial network proximity to prospective adopters, and technological progress thatreduces their relative price. Semiconductors met both conditions.