Moduli of sheaves and the Chow group of K3 surfaces

Let X be a projective complex K3 surface. Beauville and Voisin singled out a 0-cycle c_X on X of degree 1: it is represented by any point lying on a rational curve in X. Huybrechts proved that the second Chern class of a rigid simple vector-bundle on X is a multiple of the Beauville-Voisin class c_X if certain hypotheses hold and he conjectured that the additional hypotheses are unnecessary. We believe that the following generalization of Huybrechts' conjecture holds. Let M and N be moduli spaces of stable pure sheaves on X (with fixed cohomological Chern characters) and suppose that they have the same dimension: then the set whose elements are second Chern classes of sheaves parametrized by the closure of M (in the corresponding moduli spaces of semistable sheaves) is equal to the set whose elements are second Chern classes of sheaves parametrized by the closure of N after a translation by a suitable multiple of c_X (so that degrees match). We will prove that the above statement holds under some additional assumptions.Comment: Deleted a footnote and replaced it by a sentence in the main body of the pape

Periods of Double EPW-sextics

We study the indeterminacy locus of the period map for double EPW-sextics. We recall that double EPW-sextics are parametrized by lagrangian subspaces of the third wedge-product of a 6-dimensional complex vector-space. The indeterminacy locus is contained in the set of lagrangians containing a decomposable vector. The projectivization of the 3-dimensional support of such a decomposable vector contains a degeneracy subscheme which is either all of the plane or a sextic curve. We show that the period map is regular on any lagrangian A such that for all decomposables in A the corresponding degeneracy subscheme is a GIT-semistable sextic curve whose closure (in the semistable locus) does not contain a triple conic.Comment: We added a proof that the the period map of double EPW-sextics with isolated singularities is an open embedding into the complement of four explicit arithmetic divisors in the period space. Gave precise references to results of "Moduli of double EPW-sextics" (latest arXiv version) which will appear in Memoirs of the AM

Low in‑hospital mortality rate in patients with COVID‑19 receiving thromboprophylaxis: data from the multicentre observational START‑COVID Register

Abstract COVID-19 infection causes respiratory pathology with severe interstitial pneumonia and extra-pulmonary complications; in particular, it may predispose to thromboembolic disease. The current guidelines recommend the use of thromboprophylaxis in patients with COVID-19, however, the optimal heparin dosage treatment is not well-established. We conducted a multicentre, Italian, retrospective, observational study on COVID-19 patients admitted to ordinary wards, to describe clinical characteristic of patients at admission, bleeding and thrombotic events occurring during hospital stay. The strategies used for thromboprophylaxis and its role on patient outcome were, also, described. 1091 patients hospitalized were included in the START-COVID-19 Register. During hospital stay, 769 (70.7%) patients were treated with antithrombotic drugs: low molecular weight heparin (the great majority enoxaparin), fondaparinux, or unfractioned heparin. These patients were more frequently affected by comorbidities, such as hypertension, atrial fibrillation, previous thromboembolism, neurological disease,and cancer with respect to patients who did not receive thromboprophylaxis. During hospital stay, 1.2% patients had a major bleeding event. All patients were treated with antithrombotic drugs; 5.4%, had venous thromboembolism [30.5% deep vein thrombosis (DVT), 66.1% pulmonary embolism (PE), and 3.4% patients had DVT + PE]. In our cohort the mortality rate was 18.3%. Heparin use was independently associated with survival in patients aged ≥ 59 years at multivariable analysis. We confirmed the high mortality rate of COVID-19 in hospitalized patients in ordinary wards. Treatment with antithrombotic drugs is significantly associated with a reduction of mortality rates especially in patients older than 59 years

Persistent Delay Activity in Cortex: A Galilean Phase in Neuro-Physiology?

what information is available for the machine to carry out the transformations leading to the outcome. This problem does not face the designer of a device. He can apriori decide on the operands, have his system generate them, and then act upon them. This is what is done in a digital computer, and this is what happens often in simulations of cognitive systems by neural network models. But studying the brain is a quite different matter. The operands (the representations) are part of what must be discovered experimentally. And with the enormous numbers of neurons in a cortex and the extremely complex course of activity followed by each of them, this is an unenviable task. It appears to me that the only quantity of this type that we have to date, with some degree of confidence, are activities in the delay period of cognitive experiments. Those are the elevated spike rate distributions that are provoked by a given stimulus and persist after its removal until the arrival of