18 research outputs found
Calabi-Yau quotients with terminal singularities
In this paper we are interested in quotients of Calabi-Yau threefolds with
isolated singularities. In particular, we analyze the case when has
terminal singularities. We prove that, if is cyclic of prime order and
has terminal singularities, then has order or .Comment: 15 pages, no figures. Current version has some changes in the
structure of the article, some corrected typos and an up-to-date bibliograph
Covering of elliptic curves and the kernel of the Prym map
Motivated by a conjecture of Xiao, we study families of coverings of elliptic
curves and their corresponding Prym map . More precisely, we describe the
codifferential of the period map associated to in terms of the
residue of meromorphic -forms and then we use it to give a characterization
for the coverings for which the dimension of is the least possibile.
This is useful in order to exclude the existence of non isotrivial fibrations
with maximal relative irregularity and thus also in order to give
counterexamples to the Xiao's conjecture mentioned above. The first
counterexample to the original conjecture, due to Pirola, is then analysed in
our framework.Comment: 21 pages, no figures. The seminal ideas at the base of this article
were born in the framework of the PRAGMATIC project of year 201
New examples of Calabi-Yau threefolds and genus zero surfaces
We classify the subgroups of the automorphism group of the product of 4
projective lines admitting an invariant anticanonical smooth divisor on which
the action is free. As a first application, we describe new examples of
Calabi-Yau 3-folds with small Hodge numbers. In particular, the Picard number
is 1 and the number of moduli is 5. Furthermore, the fundamental group is
non-trivial. We also construct a new family of minimal surfaces of general type
with geometric genus zero, K^2=3 and fundamental group of order 16. We show
that this family dominates an irreducible component of dimension 4 of the
moduli space of the surfaces of general type.Comment: 18 pages; v2: simplified some arguments in the last section, final
version to appear on Communications in Contemporary Mathematic
Lefschetz properties for jacobian rings of cubic fourfolds and other Artinian algebras
In this paper, we exploit some geometric-differential techniques to prove the
strong Lefschetz property in degree for a complete intersection standard
Artinian Gorenstein algebra of codimension presented by quadrics. We prove
also some strong Lefschetz properties for the same kind of Artinian algebras in
higher codimensions. Moreover, we analyze some loci that come naturally into
the picture of "special" Artinian algebras: for them, we give some geometric
descriptions and show a connection between the non emptiness of the so-called
non-Lefschetz locus in degree and the "lifting" of a weak Lefschetz
property to an algebra from one of its quotients.Comment: 21 page
Clinical features and outcomes of elderly hospitalised patients with chronic obstructive pulmonary disease, heart failure or both
Background and objective: Chronic obstructive pulmonary disease (COPD) and heart failure (HF) mutually increase the risk of being present in the same patient, especially if older. Whether or not this coexistence may be associated with a worse prognosis is debated. Therefore, employing data derived from the REPOSI register, we evaluated the clinical features and outcomes in a population of elderly patients admitted to internal medicine wards and having COPD, HF or COPDâ+âHF. Methods: We measured socio-demographic and anthropometric characteristics, severity and prevalence of comorbidities, clinical and laboratory features during hospitalization, mood disorders, functional independence, drug prescriptions and discharge destination. The primary study outcome was the risk of death. Results: We considered 2,343 elderly hospitalized patients (median age 81 years), of whom 1,154 (49%) had COPD, 813 (35%) HF, and 376 (16%) COPDâ+âHF. Patients with COPDâ+âHF had different characteristics than those with COPD or HF, such as a higher prevalence of previous hospitalizations, comorbidities (especially chronic kidney disease), higher respiratory rate at admission and number of prescribed drugs. Patients with COPDâ+âHF (hazard ratio HR 1.74, 95% confidence intervals CI 1.16-2.61) and patients with dementia (HR 1.75, 95% CI 1.06-2.90) had a higher risk of death at one year. The Kaplan-Meier curves showed a higher mortality risk in the group of patients with COPDâ+âHF for all causes (pâ=â0.010), respiratory causes (pâ=â0.006), cardiovascular causes (pâ=â0.046) and respiratory plus cardiovascular causes (pâ=â0.009). Conclusion: In this real-life cohort of hospitalized elderly patients, the coexistence of COPD and HF significantly worsened prognosis at one year. This finding may help to better define the care needs of this population
A theorem of Gordan and Noether via Gorenstein rings
Gordan and Noether proved in their fundamental theorem that an hypersurface
with is a cone if and only if has
vanishing hessian (i.e. the determinant of the Hessian matrix). They also
showed that the statement is false if , by giving some
counterexamples. Since their proof, several others have been proposed in the
literature. In this paper we give a new one by using a different perspective
which involves the study of standard Artinian Gorenstein -algebras
and the Lefschetz properties. As a further application of our setting, we prove
that a standard Artinian Gorenstein algebra
with generated by a regular sequence of quadrics has the strong Lefschetz
property. In particular, this holds for Jacobian rings associated to smooth
cubic threefolds.Comment: 21 page