Induced automorphisms on irreducible symplectic manifolds

We introduce the notion of induced automorphisms in order to state a criterion to determine whether a given automorphism on a manifold of K3[n]-type is, in fact, induced by an automorphism of a K3 surface, and the manifold is a moduli space of stable objects on the K3. This criterion is applied to the classification of non-symplectic prime order automorphisms on manifolds of K3[2]-type, and we prove that almost all cases are covered. Variations of this notion and the above criterion are introduced and discussed for the other known deformation types of irreducible symplectic manifolds. Furthermore, we provide a description of the picard lattice of several irreducible symplectic manifolds having a lagrangian fibration

Gushel–Mukai varieties with many symmetries and an explicit irrational Gushel–Mukai threefold

We construct an explicit smooth Fano complex threefold with Picard number 1, index 1, and degree 10 (also known as a Gushel–Mukai threefold) and prove that it is not rational by showing that its intermediate Jacobian has a faithful PSL(2,F11)-action. Along the way, we construct Gushel–Mukai varieties of various dimensions with rather large (finite) automorphism groups. The starting point of all these constructions is an Eisenbud–Popescu–Walter sextic with a faithful PSL(2,F11)-action discovered by the second author in 2013

Fano varieties of K3 type and IHS manifolds

We construct several new families of Fano varieties of K3 type. We give a geometrical explanation of the K3 structure and we link some of them to projective families of irreducible holomorphic symplectic manifolds

Symplectic involutions of K3[n] type and Kummer n type manifolds

In this paper, we describe the fixed locus of a symplectic involution on a hyper-Kahler manifold of type K3([n]) or of Kummer n type. We prove that the fixed locus consists of finitely many copies of deformations of Hilbert schemes of K3 surfaces of lower dimensions and isolated fixed points

Deformations of rational curves on primitive symplectic varieties and applications

We study the deformation theory of rational curves on primitive symplectic varieties and show that if the rational curves cover a divisor, then, as in the smooth case, they deform along their Hodge locus in the universal locally trivial deformation. As applica-tions, we extend Markman's deformation invariance of prime exceptional divisors along their Hodge locus to this singular framework and provide existence results for uniruled ample divisors on primitive symplectic varieties that are locally trivial deformations of any moduli space of semistable objects on a projective K3 or fibers of the Albanese map of those on an abelian surface. We also present an application to the existence of prime exceptional divisors

Severi varieties and Brill-Noether theory of curves on abelian surfaces

Severi varieties and Brill-Noether theory of curves on K3 surfaces are well understood. Yet, quite little is known for curves on abelian surfaces. Given a general abelian surface $S$ with polarization $L$ of type $(1,n)$, we prove nonemptiness and regularity of the Severi variety parametrizing $\delta$-nodal curves in the linear system $|L|$ for $0\leq \delta\leq n-1=p-2$ (here $p$ is the arithmetic genus of any curve in $|L|$). We also show that a general genus $g$ curve having as nodal model a hyperplane section of some $(1,n)$-polarized abelian surface admits only finitely many such models up to translation; moreover, any such model lies on finitely many $(1,n)$-polarized abelian surfaces. Under certain assumptions, a conjecture of Dedieu and Sernesi is proved concerning the possibility of deforming a genus $g$ curve in $S$ equigenerically to a nodal curve. The rest of the paper deals with the Brill-Noether theory of curves in $|L|$. It turns out that a general curve in $|L|$ is Brill-Noether general. However, as soon as the Brill-Noether number is negative and some other inequalities are satisfied, the locus $|L|^r_d$ of smooth curves in $|L|$ possessing a $g^r_d$ is nonempty and has a component of the expected dimension. As an application, we obtain the existence of a component of the Brill-Noether locus $\mathcal{M}^r_{p,d}$ having the expected codimension in the moduli space of curves $\mathcal{M}_p$. For $r=1$, the results are generalized to nodal curves

Curve classes on irreducible holomorphic symplectic varieties

We prove that the integral Hodge conjecture holds for 1-cycles on irreducible holomorphic symplectic varieties of K3 type and of Generalized Kummer type. As an application, we give a new proof of the integral Hodge conjecture for cubic fourfolds.Comment: 15 page

Organizational citizenship behaviour as a protective factor against the occurrence of adverse nursing-sensitive outcomes: a multilevel investigation

Aims This study aimed to investigate the association between organizational citizenship behaviour enacted by nurses and the occurrence of adverse nursing-sensitive patient outcomes. Background Managing psychosocial factors (i.e., aspects concerning the work environment) is key to ensure patient safety, to prevent exacerbation of case complexity and to cope with critical shortages in human and financial resources. Methods Self-report measures of nurses' organizational citizenship behaviour were combined with objective data on the incidence of adverse nursing-sensitive outcomes (i.e., pressure ulcers and restraint use) collected through patients' medical records. Participants were 11,345 patients and 1346 nurses across 52 teams working in 14 Italian hospitals. Data were analysed using multilevel binary logistic regression models. Results A negative relationship between nurses' organizational citizenship behaviour and restraint use was identified, with an odds ratio of 0.11. Thus, for a one-unit higher organizational citizenship behaviour score, the odds of using restraints shrink to about one eighth of the previous level. Conclusions Intervention strategies to foster the implementation of organizational citizenship behaviour among nurses may inhibit the occurrence of critical outcomes affecting patients' health and well-being (i.e., using restraint devices). Implications for Nursing Management In health care organizations, shaping a psychosocial environment encouraging organizational citizenship behaviour can mitigate the occurrence of adverse nursing-sensitive outcomes such as restraint use on patients

Software Model Checking with Explicit Scheduler and Symbolic Threads

In many practical application domains, the software is organized into a set of threads, whose activation is exclusive and controlled by a cooperative scheduling policy: threads execute, without any interruption, until they either terminate or yield the control explicitly to the scheduler. The formal verification of such software poses significant challenges. On the one side, each thread may have infinite state space, and might call for abstraction. On the other side, the scheduling policy is often important for correctness, and an approach based on abstracting the scheduler may result in loss of precision and false positives. Unfortunately, the translation of the problem into a purely sequential software model checking problem turns out to be highly inefficient for the available technologies. We propose a software model checking technique that exploits the intrinsic structure of these programs. Each thread is translated into a separate sequential program and explored symbolically with lazy abstraction, while the overall verification is orchestrated by the direct execution of the scheduler. The approach is optimized by filtering the exploration of the scheduler with the integration of partial-order reduction. The technique, called ESST (Explicit Scheduler, Symbolic Threads) has been implemented and experimentally evaluated on a significant set of benchmarks. The results demonstrate that ESST technique is way more effective than software model checking applied to the sequentialized programs, and that partial-order reduction can lead to further performance improvements.Comment: 40 pages, 10 figures, accepted for publication in journal of logical methods in computer scienc