This article analyses the behaviour of analytic cycles on deformations of strictly pseudoconvex surfaces. As a preliminary result we show that a relatively compact strictly pseudoconvex surface is the union of two Stein open subsets. The main result of the article is that there is a small deformation of a minimal relatively compact strictly pseudoconvex surface that has no positive dimensional analytic cycles, hence is Stein. We also prove that a strictly pseudoconvex surface contains a semiregular 1-dimensional cycle if it contains one 1-dim cycle. In the last section the main result is applied to the study of contact structures of three dimensional manifolds.

Background: Critically ill patients with COVID-19 are prone to develop severe acute kidney injury (AKI), defined as KDIGO (Kidney Disease Improving Global Outcomes) stages 2 or 3. However, data are limited in these patients. We aimed to report the incidence, risk factors, and prognostic impact of severe AKI in critically ill patients with COVID-19 admitted to the intensive care unit (ICU) for acute respiratory failure. Methods: A retrospective monocenter study including adult patients with laboratory-confirmed severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) infection admitted to the ICU for acute respiratory failure. The primary outcome was to identify the incidence and risk factors associated with severe AKI (KDIGO stages 2 or 3). Results: Overall, 110 COVID-19 patients were admitted. Among them, 77 (70%) required invasive mechanical ventilation (IMV), 66 (60%) received vasopressor support, and 9 (8.2%) needed extracorporeal membrane oxygenation (ECMO). Severe AKI occurred in 50 patients (45.4%). In multivariable logistic regression analysis, severe AKI was independently associated with age (odds ratio (OR) = 1.08 (95% CI (confidence interval): 1.03–1.14), p = 0.003), IMV (OR = 33.44 (95% CI: 2.20–507.77), p = 0.011), creatinine level on admission (OR = 1.04 (95% CI: 1.008–1.065), p = 0.012), and ECMO (OR = 11.42 (95% CI: 1.95–66.70), p = 0.007). Inflammatory (interleukin-6, C-reactive protein, and ferritin) or thrombotic (D-dimer and fibrinogen) markers were not associated with severe AKI after adjustment for potential confounders. Severe AKI was independently associated with hospital mortality (OR = 29.73 (95% CI: 4.10–215.77), p = 0.001) and longer hospital length of stay (subhazard ratio = 0.26 (95% CI: 0.14–0.51), p < 0.001). At the time of hospital discharge, 74.1% of patients with severe AKI who were discharged alive from the hospital recovered normal or baseline renal function. Conclusion: Severe AKI was common in critically ill patients with COVID-19 and was not associated with inflammatory or thrombotic markers. Severe AKI was an independent risk factor of hospital mortality and hospital length of stay, and it should be rapidly recognized during SARS-CoV-2 infection.

Abstract. We show that a nodal hypersurface X in P 3 of degree d with a sufficiently large number l of nodes, l > 8 3, is algebraically quasi-hyperbolic, i.e. X can only have finitely many rational and elliptic curves. Our results use the theory of symmetric differentials and algebraic foliations and give a very striking example of the jumping of the number of symmetric differentials in families. IntroductionA compact analytic variety X is said to be Kobayashi hyperbolic (Brody) if it does not contain any entire curves, i.e. there are no nonconstant holomorphic mappings f : C → X. The algebraic version of the Kobayashi's conjecture states that the general hypersurface X of P 3 of degree ≥ 5 does not contain any rational or elliptic curves, i.e. X is algebraically hyperbolic. The algebraic version is, a priori, weaker but Green and Griffiths [GrGr80] formulated a conjecture which reduces the Kobayashi's hyperbolicity of X to the algebraic hyperbolicity of X. More generally and in a broader direction,

This paper using a geometric approach produces vanishing and nonvanishing results concerning the spaces of twisted symmetric differentials H 0 (X, S m Ω 1 X ⊗ O X (k)) on subvarieties X ⊂ P N , with k ≤ m. Emphasis is given to the case of k = m which is special and whose nonvanishing results on the dimensional range dim X > 2/3(N − 1) are related to the space of quadrics containing X and the variety of all tangent trisecant lines of X. The paper ends with an application showing that the twisted symmetric plurigenera,Xt ⊗ αK Xt )) along smooth families of projective varieties X t are not invariant even for α arbitrarily large. IntroductionIn this article we prove vanishing and nonvanishing results about the space of twisted symmetric differentials of subvarieties X ⊂ P N , H 0 (X, S m Ω 1 X ⊗ O X (k)) with k ≤ m (via a geometric approach). Emphasis is given to the case of k = m which is special and whose nonvanishing results on the dimensional range dim X > 2/3(N − 1) are related to the space of quadrics containing X and lead to interesting geometrical objects associated to X, as for example the variety of all tangent trisecant lines of X. The same techniques give results on the symmetric differentials of subvarieties of abelian varieties. The paper ends with an application concerning the jumping of the twisted symmetric plurigenera,