On degenerations of fiber spaces of curves of genus ≧ 2

In this note, we show that for surfaces admitting suitable fibrations, any given degeneration script x sign/Δ is bimeromorphic to a fiber space over a curve Y/Δ and we apply this result to the study of the degenerate fiber

Generalized Shioda-Inose structures on K3 surfaces

In this note, we study the action of finite groups of symplectic automorphisms on K3 surfaces which yield quotients birational to generalized Kummer surfaces. For each possible group, we determine the Picard number of the K3 surface admitting such an action and for singular K3 surfaces we show the uniqueness of the associated abelian surface

Computing heights via limits of Hodge structures

We consider the problem of explicitly computing Beilinson–Bloch heights of homologically trivial cycles on varieties defined over number fields. Recent results have established a congruence, up to the rational span of logarithms of primes, between the height of certain limit mixed Hodge structures and certain Beilinson–Bloch heights obtained from odd-dimensional hypersurfaces with a node. This congruence suggests a new method to compute Beilinson–Bloch heights. Here we explain how to compute the relevant limit mixed Hodge structures in practice, then apply our computational method to a nodal quartic curve and a nodal cubic threefold. In both cases we explain the nature of the primes occurring in the congruence.Number theory, Algebra and Geometr

Quantum Pieri rules for isotropic Grassmannians

We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew-symmetric form. We establish Pieri rules for the classical cohomology and the small quantum cohomology ring of these varieties, which give a combinatorial formula for the product of any Schubert class with certain special Schubert classes. We also give presentations of these rings, with integer coefficients, in terms of special Schubert class generators and relations.Comment: 59 pages, LaTeX, 6 figure

Age- and region-specific hepatitis B prevalence in Turkey estimated using generalized linear mixed models: a systematic review

Toy M, Önder FO, Wörmann T, et al. Age- and region-specific hepatitis B prevalence in Turkey estimated using generalized linear mixed models: a systematic review. BMC infectious diseases. 2011;11(1): 337.BACKGROUND: To provide a clear picture of the current hepatitis B situation, the authors performed a systematic review to estimate the age- and region-specific prevalence of chronic hepatitis B (CHB) in Turkey. METHODS: A total of 339 studies with original data on the prevalence of hepatitis B surface antigen (HBsAg) in Turkey and published between 1999 and 2009 were identified through a search of electronic databases, by reviewing citations, and by writing to authors. After a critical assessment, the authors included 129 studies, divided into categories: 'age-specific'; 'region-specific'; and 'specific population group'. To account for the differences among the studies, a generalized linear mixed model was used to estimate the overall prevalence across all age groups and regions. For specific population groups, the authors calculated the weighted mean prevalence. RESULTS: The estimated overall population prevalence was 4.57, 95% confidence interval (CI): 3.58, 5.76, and the estimated total number of CHB cases was about 3.3 million. The outcomes of the age-specific groups varied from 2.84, (95% CI: 2.60, 3.10) for the 0-14-year olds to 6.36 (95% CI: 5.83, 6.90) in the 25-34-year-old group. CONCLUSION: There are large age-group and regional differences in CHB prevalence in Turkey, where CHB remains a serious health problem

A triple intersection theorem for the varieties SO(n)/Pd

We study the Schubert calculus on the space of d-dimensional linear subspaces of a smooth n-dimensional quadric lying in the projective space. Following Hodge and Pedoe we develop the intersection theory of this space in a purely combinatorial manner. We prove in particular that if a triple intersection of Schubert cells on this space is nonempty then a certain combinatorial relation holds among the Schubert symbols involved, similar to the classical one. We also show when these necessary conditions are also sufficient to obtain a nontrivial intersection. Several examples are calculated to illustrate the main results

On generalized Shioda - Inose structures

[No abstract available

Heights on curves and limits of Hodge structures

We exhibit a precise connection between Néron–Tate heights on smooth curves and biextension heights of limit mixed Hodge structures associated to smoothing deformations of singular quotient curves. Our approach suggests a new way to compute Beilinson–Bloch heights in higher dimensions.Number theory, Algebra and Geometr