Points of order two on theta divisors

We give a bound on the number of points of order two on the theta divisor of a principally polarized abelian variety A. When A is the Jacobian of a curve C the result can be applied in estimating the number of effective square roots of a fixed line bundle on C.Comment: 4 page

Prym varieties of double coverings of elliptic curves

We prove the generic injectivity of the Prym map $\mathscr{P}: \mathcal{R}_{1, r} \rightarrow \mathcal{A}_{\frac{r}{2}}^\delta$ sending a double covering of an elliptic curve ramified at $r \geq 6$ points to its polarized Prym variety. For $r=6$ the map is birational and both $\mathcal{R}_{1,6}$ and $\mathcal{A}_3^\delta$ are unirational

Generic Torelli theorem for Prym varieties of ramified coverings

In this paper we prove that the Prym map, from the space of double coverings of a curve of genus g with r branch points to the moduli space of abelian varieties, is generically injective if r>6 and g>1, r=6 and g>2, r=4 and g>4, r=2 and g>5. We also show that a very generic Prym variety of dimension at least 4 is not isogenous to a Jacobian.Comment: 24 pages, 2 figures. One reference added. To appear in Compositio Mathematic

Evaluation of the performance of Dutch Lipid Clinic Network score in an Italian FH population: The LIPIGEN study

Background and aims: Familial hypercholesterolemia (FH) is an inherited disorder characterized by high levels of blood cholesterol from birth and premature coronary heart disease. Thus, the identification of FH patients is crucial to prevent or delay the onset of cardiovascular events, and the availability of a tool helping with the diagnosis in the setting of general medicine is essential to improve FH patient identification. Methods: This study evaluated the performance of the Dutch Lipid Clinic Network (DLCN) score in FH patients enrolled in the LIPIGEN study, an Italian integrated network aimed at improving the identification of patients with genetic dyslipidaemias, including FH. Results: The DLCN score was applied on a sample of 1377 adults (mean age 42.9 ± 14.2 years) with genetic diagnosis of FH, resulting in 28.5% of the sample classified as probable FH and 37.9% as classified definite FH. Among these subjects, 43.4% had at least one missing data out of 8, and about 10.0% had 4 missing data or more. When analyzed based on the type of missing data, a higher percentage of subjects with at least 1 missing data in the clinical history or physical examination was classified as possible FH (DLCN score 3–5). We also found that using real or estimated pre-treatment LDL-C levels may significantly modify the DLCN score. Conclusions: Although the DLCN score is a useful tool for physicians in the diagnosis of FH, it may be limited by the complexity to retrieve all the essential information, suggesting a crucial role of the clinical judgement in the identification of FH subjects