24 research outputs found
Normality and smoothness of simple linear group compactifications
If G is a complex semisimple algebraic group, we characterize the normality
and the smoothness of its simple linear compactifications, namely those
equivariant GxG-compactifications which possess a unique closed orbit and which
arise in a projective space of the shape P(End(V)), where V is finite
dimensional rational G-module. Both the characterizations are purely
combinatorial and are expressed in terms of the highest weights of V. In
particular, we show that Sp(2r) (with r > 0) is the unique non-adjoint simple
group which admits a simple smooth compactification.Comment: v2: minor changes, final version. To appear in Math.
COVID-19 symptoms at hospital admission vary with age and sex: results from the ISARIC prospective multinational observational study
Background:
The ISARIC prospective multinational observational study is the largest cohort of hospitalized patients with COVID-19. We present relationships of age, sex, and nationality to presenting symptoms.
Methods:
International, prospective observational study of 60â109 hospitalized symptomatic patients with laboratory-confirmed COVID-19 recruited from 43 countries between 30 January and 3 August 2020. Logistic regression was performed to evaluate relationships of age and sex to published COVID-19 case definitions and the most commonly reported symptoms.
Results:
âTypicalâ symptoms of fever (69%), cough (68%) and shortness of breath (66%) were the most commonly reported. 92% of patients experienced at least one of these. Prevalence of typical symptoms was greatest in 30- to 60-year-olds (respectively 80, 79, 69%; at least one 95%). They were reported less frequently in children (â€â18 years: 69, 48, 23; 85%), older adults (â„â70 years: 61, 62, 65; 90%), and women (66, 66, 64; 90%; vs. men 71, 70, 67; 93%, each Pâ<â0.001). The most common atypical presentations under 60 years of age were nausea and vomiting and abdominal pain, and over 60 years was confusion. Regression models showed significant differences in symptoms with sex, age and country.
Interpretation:
This international collaboration has allowed us to report reliable symptom data from the largest cohort of patients admitted to hospital with COVID-19. Adults over 60 and children admitted to hospital with COVID-19 are less likely to present with typical symptoms. Nausea and vomiting are common atypical presentations under 30 years. Confusion is a frequent atypical presentation of COVID-19 in adults over 60 years. Women are less likely to experience typical symptoms than men
Homogeneous Spaces and Equivariant Embeddings
Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory. By standard reasons of algebraic geometry, in order to solve various problems on a homogeneous space it is natural and helpful to compactify it keeping track of the group action, i.e. to consider equivariant completions or, more generally, open embeddings of a given homogeneous space. Such equivariant embeddings are the subject of this book. We focus on classification of equivariant e
Flexible affine cones and flexible coverings
We provide a new criterion for flexibility of affine cones over varieties covered by flexible affine varieties.We apply this criterion to prove flexibility of affine cones over secant varieties of SegreâVeronese embeddings and over certain Fano threefolds. We further prove flexibility of total coordinate spaces of Cox rings of del Pezzo surfaces.publishe