On the Hilbert scheme of curves in higher-dimensional projective space

In this paper we prove that, for any $n\ge 3$, there exist infinitely many $r\in \N$ and for each of them a smooth, connected curve $C_r$ in $\P^r$ such that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme \hilb(\P^r). This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type.Comment: latex, 12 pages, no figure

The orbifold cohomology of moduli of genus 3 curves

In this work we study the additive orbifold cohomology of the moduli stack of smooth genus g curves. We show that this problem reduces to investigating the rational cohomology of moduli spaces of cyclic covers of curves where the genus of the covering curve is g. Then we work out the case of genus g=3. Furthermore, we determine the part of the orbifold cohomology of the Deligne-Mumford compactification of the moduli space of genus 3 curves that comes from the Zariski closure of the inertia stack of M_3.Comment: 29 pages, 2 figures. Minor changes, to appear in Manuscripta Mat

Derived categories of Burniat surfaces and exceptional collections

We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all Burniat surfaces. The semiorthogonal complement $\mathcal A$ of $\Upsilon$ is an "almost phantom" category: it has trivial Hochschild homology, and K_0(\mathcal A)=\bZ_2^6.Comment: 15 pages, 1 figure; further remarks expande

Magnetic excitations and electronic interactions in Sr2_2CuTeO6_6: a spin-1/2 square lattice Heisenberg antiferromagnet

Sr$_2$CuTeO$_6$ presents an opportunity for exploring low-dimensional magnetism on a square lattice of $S=1/2$ Cu$^{2+}$ ions. We employ ab initio multi-reference configuration interaction calculations to unravel the Cu$^{2+}$ electronic structure and to evaluate exchange interactions in Sr$_2$CuTeO$_6$. The latter results are validated by inelastic neutron scattering using linear spin-wave theory and series-expansion corrections for quantum effects to extract true coupling parameters. Using this methodology, which is quite general, we demonstrate that Sr$_2$CuTeO$_6$ is an almost realization of a nearest-neighbor Heisenberg antiferromagnet but with relatively weak coupling of 7.18(5) meV.Comment: 10 pages, 7 figure

Explicit and implicit own’s body and space perception in painful musculoskeletal disorders and rheumatic diseases: a systematic scoping review

Background: Pain and body perception are essentially two subjective mutually influencing experiences. However, in the field of musculoskeletal disorders and rheumatic diseases we lack of a comprehensive knowledge about the relationship between body perception dysfunctions and pain or disability. We systematically mapped the literature published about the topics of: a) somatoperception; b) body ownership; and c) perception of space, analysing the relationship with pain and disability. The results were organized around the two main topics of the assessment and treatment of perceptual dysfunctions. Methods: This scoping review followed the six-stage methodology suggested by Arksey and O’Malley. Ten electronic databases and grey literature were systematically searched. The PRISMA Extension for Scoping Reviews was used for reporting results. Two reviewers with different background, independently performed study screening and selection, and one author performed data extraction, that was checked by a second reviewer. Results: Thirty-seven studies fulfilled the eligibility criteria. The majority of studies (68%) concerned the assessment methodology, and the remaining 32% investigated the effects of therapeutic interventions. Research designs, methodologies adopted, and settings varied considerably across studies. Evidence of distorted body experience were found mainly for explicit somatoperception, especially in studies adopting self-administered questionnaire and subjective measures, highlighting in some cases the presence of sub-groups with different perceptual features. Almost half of the intervention studies (42%) provided therapeutic approaches combining more than one perceptual task, or sensory-motor tasks together with perceptual strategies, thus it was difficult to estimate the relative effectiveness of each single therapeutic component. Conclusions: To our knowledge, this is the first attempt to systematically map and summarize this research area in the field of musculoskeletal disorders and rheumatic diseases. Although methodological limitations limit the validity of the evidence obtained, some strategies of assessment tested and therapeutic strategies proposed represent useful starting points for future research. This review highlights preliminary evidence, strengths, and limitations of the literature published about the research questions, identifying key points that remain opened to be addressed, and make suggestions for future research studies. Body representation, as well as pain perception and treatment, can be better understood if an enlarged perspective including body and space perception is considered