On the structure of the fibers of truncation morphisms

Let k be an algebraically closed field and let X be a separated scheme of finite type over k of pure dimension d. We study the structure of the fibres of the truncation morphisms from the arc space of X to jet spaces of X and also between jet spaces. Our results are generalizations of results of Denef, Loeser, Ein and Mustata. We will use them to find the optimal lower bound for the poles of the motivic zeta function associated to an arbitrary ideal.Comment: 18 pages, to appear in the Bulletin of the London Mathematical Societ

Geometric motivic Poincar\'e series of quasi-ordinary singularities

The geometric motivic Poincar\'e series of a germ $(S,0)$ of complex algebraic variety takes into account the classes in the Grothendieck ring of the jets of arcs through $(S,0)$. Denef and Loeser proved that this series has a rational form. We give an explicit description of this invariant when $(S,0)$ is an irreducible germ of quasi-ordinary hypersurface singularity in terms of the Newton polyhedra of the logarithmic jacobian ideals. These ideals are determined by the characteristic monomials of a quasi-ordinary branch parametrizing $(S,0)$

Arcs and jets on toric singularities and quasi-ordinary singularities

Abstracts from the workshop held January 29--February 4, 2006Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu

Motivic Poincaré series, toric singularities and logarithmic Jacobian ideals

The geometric motivic Poincare series of a variety, which was introduced by Denef and Loeser, takes into account the classes in the Grothendieck ring of the sequence of jets of arcs in the variety. Denef and Loeser proved that this series has a rational form. We describe it in the case of an affine toric variety of arbitrary dimension. The result, which provides an explicit set of candidate poles, is expressed in terms of the sequence of Newton polyhedra of certain monomial ideals,which we call logarithmic Jacobian ideals, associated to the modules of differential forms with logarithmic poles outside the torus of the toric variety

Serum Potassium Dynamics During Acute Heart Failure Hospitalization

[Abstract] Background. Available information about prognostic implications of potassium levels alteration in the setting of acute heart failure (AHF) is scarce. Objectives. We aim to describe the prevalence of dyskalemia (hypo or hyperkalemia), its dynamic changes during AHF-hospitalization, and its long-term clinical impact after hospitalization. Methods. We analyzed 1779 patients hospitalized with AHF who were included in the REDINSCOR II registry. Patients were classified in three groups, according to potassium levels both on admission and discharge: hypokalemia (potassium  5 mEq/L). Results. The prevalence of hypokalemia and hyperkalemia on admission was 8.2 and 4.6%, respectively, and 6.4 and 2.7% at discharge. Hyperkalemia on admission was associated with higher in-hospital mortality (OR = 2.32 [95% CI: 1.04–5.21] p = 0.045). Among patients with hypokalemia on admission, 79% had normalized potassium levels at discharge. In the case of patients with hyperkalemia on admission, 89% normalized kalemia before discharge. In multivariate Cox regression, dyskalemia was associated with higher 12-month mortality, (HR = 1.48 [95% CI, 1.12–1.96], p = 0.005). Among all patterns of dyskalemia persistent hypokalemia (HR = 3.17 [95% CI: 1.71–5.88]; p < 0.001), and transient hyperkalemia (HR = 1.75 [95% CI: 1.07–2.86]; p = 0.023) were related to reduced 12-month survival. Conclusions. Potassium levels alterations are frequent and show a dynamic behavior during AHF admission. Hyperkalemia on admission is an independent predictor of higher in-hospital mortality. Furthermore, persistent hypokalemia and transient hyperkalemia on admission are independent predictors of 12-month mortality.This work is funded by the Instituto de Salud Carlos III (Ministry of Economy, Industry, and Competitiveness) and co-funded by the European Regional Development Fund, through the CIBER in cardiovascular diseases (CB16/11/00502)

Nephrin mutations cause childhood- and adult-onset focal segmental glomerulosclerosis

Mutations in the NPHS1 gene cause congenital nephrotic syndrome of the Finnish type presenting before the first 3 months of life. Recently, NPHS1 mutations have also been identified in childhood-onset steroid-resistant nephrotic syndrome and milder courses of disease, but their role in adults with focal segmental glomerulosclerosis remains unknown. Here we developed an in silico scoring matrix to evaluate the pathogenicity of amino-acid substitutions using the biophysical and biochemical difference between wild-type and mutant amino acid, the evolutionary conservation of the amino-acid residue in orthologs, and defined domains, with the addition of contextual information. Mutation analysis was performed in 97 patients from 89 unrelated families, of which 52 presented with steroid-resistant nephrotic syndrome after 18 years of age. Compound heterozygous or homozygous NPHS1 mutations were identified in five familial and seven sporadic cases, including one patient 27 years old at onset of the disease. Substitutions were classified as ‘severe’ or ‘mild’ using this in silico approach. Our results suggest an earlier onset of the disease in patients with two ‘severe’ mutations compared to patients with at least one ‘mild’ mutation. The finding of mutations in a patient with adult-onset focal segmental glomerulosclerosis indicates that NPHS1 analysis could be considered in patients with later onset of the disease

Estabilidad del fibrado universal restringido a congruencias

Esta tesis se ocupa de contribuir al problema de determinar si, dados dos enteros arbitrarios a y b, existe una congruencia de G(1,3) con bigrado (a,b). Dolgachev y Reider introdujeron un modo de encontrar restricciones para el bigrado de una congruencia S, consistente en estudiar la semiestabilidad del fibrado universal cociente sobre G(1,3) restringido a S, Q│S. En concreto, conjeturaron que si S es una congruencia no degenerada como superficie de P^5, entonces el fibrado Q│S es semiestable. Un paso previo al estudio de la estabilidad de un fibrado es el estudio de su simplicidad. En la presente tesis se demuestra que sólo hay cuatro tipos de congruencias en la Grassmanniana G(1,3) para las que el fibrado universal Q restringido no es simple. De aquí se deduce en particular que Q no es simple si y sólo si es escindido. Con respecto al problema de la estabilidad, en esta tesis se demuestra un resultado mediante el cual se deducen condiciones geométricas para una congruencia S dependiendo de la pendiente de un subhaz lineal saturado de Q│S. También se comprueba que la conjetura de Dolgachev y Reider es cierta para las congruencias de grado menor o igual que 10, calculando además la pendiente máxima que alcanzan los subhaces lineales de Q│S para cada congruencia S de grado menor o igual que 9