On the symplectic eightfold associated to a Pfaffian cubic fourfold

We show that the irreducible holomorphic symplectic eightfold Z associated to a cubic fourfold Y not containing a plane is deformation-equivalent to the Hilbert scheme of four points on a K3 surface. We do this by constructing for a generic Pfaffian cubic Y a birational map Z ---> Hilb^4(X), where X is the K3 surface associated to Y by Beauville and Donagi. We interpret Z as a moduli space of complexes on X and observe that at some point of Z, hence on a Zariski open subset, the complex is just the ideal sheaf of four points.Comment: 9 pages. Minor changes; to appear in Crelle as an appendix to 1305.017

Hodge theory and derived categories of cubic fourfolds

Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics - conjecturally, the ones that are rational - have specific K3s associated to them geometrically. Hassett has studied cubics with K3s associated to them at the level of Hodge theory, and Kuznetsov has studied cubics with K3s associated to them at the level of derived categories. These two notions of having an associated K3 should coincide. We prove that they coincide generically: Hassett's cubics form a countable union of irreducible Noether-Lefschetz divisors in moduli space, and we show that Kuznetsov's cubics are a dense subset of these, forming a non-empty, Zariski open subset in each divisor.Comment: 37 pages. Applications to algebraic cycles added, and other improvements following referees' suggestions. This is a slightly expanded version of the paper to appear in Duke Math

Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences

We show that for many moduli spaces M of torsion sheaves on K3 surfaces S, the functor D(S) -> D(M) induced by the universal sheaf is a P-functor, hence can be used to construct an autoequivalence of D(M), and that this autoequivalence can be factored into geometrically meaningful equivalences associated to abelian fibrations and Mukai flops. Along the way we produce a derived equivalence between two compact hyperkaehler 2g-folds that are not birational, for every g >= 2. We also speculate about an approach to showing that birational moduli spaces of sheaves on K3 surfaces are derived-equivalent.Comment: 28 pages. typos corrected. final version to appear in JLM

Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces

We provide explicit descriptions of the generic members of Hassett's divisors $\mathcal C_d$ for relevant $18\leq d\leq 38$ and for $d=44$. In doing so, we prove that $\mathcal C_d$ is unirational for $18\leq d\leq 38,d=44$. As a corollary, we prove that the moduli space $\mathcal N_{d}$ of polarized K3 surfaces of degree $d$ is unirational for $d=14,26,38$. The case $d=26$ is entirely new, while the other two cases have been previously proven by Mukai.Comment: 13 pages, 2 tables. Script for the computer calculations used are provided on the author's websit

Hodge numbers are not derived invariants in positive characteristic

We study a pair of Calabi-Yau threefolds X and M, fibered in non-principally polarized Abelian surfaces and their duals, and an equivalence D^b(X) = D^b(M), building on work of Gross, Popescu, Bak, and Schnell. Over the complex numbers, X is simply connected while pi_1(M) = (Z/3)^2. In characteristic 3, we find that X and M have different Hodge numbers, which would be impossible in characteristic 0. In an appendix, we give a streamlined proof of Abuaf's result that the ring H^*(O) is a derived invariant of complex threefolds and fourfolds. A second appendix by Alexander Petrov gives a family of higher-dimensional examples to show that h^{0,3} is not a derived invariant in any positive characteristic

Formulation de cas dans la psychose débutante : Quels outils pour le travail en équipe? [Case Formulation in Early Psychosis: What are the Tools for Teamwork?]

Nous présentons d’abord brièvement le programme TIPP et les concepts généraux de la prise en charge précoce dans la psychose débutante. Un des objectifs de l’intervention dans la phase précoce des troubles psychotiques est notamment de proposer des soins spécifiques adaptés à cette phase de la maladie. En début de prise en charge, l’équipe de soins et en particulier le gestionnaire de cas (case manager), chef d’orchestre de la prise en charge, sont confrontés à une quantité importante d’information dont il faut dégager les lignes de forces pour mettre en place une prise en charge adaptée. Cet article propose un modèle qui peut constituer un outil de travail précieux pour les équipes travaillant dans l’intervention précoce pour faire émerger une formulation de cas et synthétiser les situations cliniques des patients, en extraire une histoire qui fasse sens et ainsi faciliter la mise en place d’un projet thérapeutique

Substance use in clinical high risk for psychosis: a review of the literature

AimIn the literature, there is evidence suggesting an association between substance use and psychosis. However, little is known about substance use in those who may be in the pre-psychotic phase, that is, those who are putatively prodromal are considered to be at clinical high risk (CHR) of developing psychosis. MethodsWe conducted a review of publications measuring patterns and rates of substance use in CHR for psychosis individuals and the effects on the transition to psychosis. ResultsOf 5527 potentially relevant research papers, 10 met inclusion criteria of CHR subjects and specifically mentioned substance use in the sample. The results of these studies varied. Cannabis, alcohol and tobacco/nicotine were reported as the most commonly used substances. There was limited information on the changes in patterns of use over time. Two out of the ten studies found a significant association between the use of substances and subsequent transition to psychosis. In one of these studies, substance abuse was a predictor of psychosis when included as a variable in a prediction algorithm. In the other study, the abuse of cannabis and nicotine was associated with transition to psychosis. ConclusionsWe found limited evidence to suggest that increased rates of substance use may be associated with transition to psychosis. However, further prospective research examining the association between substance use and transition to psychosis is required before any firm conclusions can be made

Are lay people good at recognising the symptoms of schizophrenia?

©2013 Erritty, Wydell. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.This article has been made available through the Brunel Open Access Publishing Fund.Aim: The aim of this study was to explore the general public’s perception of schizophrenia symptoms and the need to seekhelp for symptoms. The recognition (or ‘labelling’) of schizophrenia symptoms, help-seeking behaviours and public awareness of schizophrenia have been suggested as potentially important factors relating to untreated psychosis. Method: Participants were asked to rate to what extent they believe vignettes describing classic symptoms (positive and negative) of schizophrenia indicate mental illness. They were also asked if the individuals depicted in the vignettes required help or treatment and asked to suggest what kind of help or treatment. Results: Only three positive symptoms (i.e., Hallucinatory behaviour, Unusual thought content and Suspiciousness) of schizophrenia were reasonably well perceived (above 70%) as indicating mental illness more than the other positive or negative symptoms. Even when the participants recognised that the symptoms indicated mental illness, not everyone recommended professional help. Conclusion: There may be a need to improve public awareness of schizophrenia and psychosis symptoms, particularly regarding an awareness of the importance of early intervention for psychosis