A Lower Bound on the Euler–Poincaré Characteristic of Certain Surfaces of General Type with a Linear Pencil of Hyperelliptic Curves

Let S be a surface of general type. In this article, when there exists a relatively minimal hyperelliptic fibration whose slope is less than or equal to four, we give a lower bound on the Euler–Poincaré characteristic of S. Furthermore, we prove that our bound is the best possible by giving required hyperelliptic fibrations.

Pencil-thin ependymal enhancement in neuromyelitis optica spectrum disorders

AQP4 water channels are thought to be the target of autoimmune attack in neuromyelitis optica-spectrum disorders (NMOsd). AQP4 are highly expressed on ventricular ependyma. The objective of this study was to describe a novel pattern of linear, ‘pencil-thin’ enhancement of ventricular ependyma in NMOsd. We report two NMOsd patients with pencil-thin ependymal enhancement along the frontal and occipital horns of lateral ventricles. Differential diagnosis of ependymal enhancement should include NMOsd alongside with infectious and neoplastic etiologies. Pencil-thin ependymal enhancement may be a helpful radiological marker of NMOsd that can be used to differentiate this condition from multiple sclerosis.

FIBERS OF PENCILS OF CURVES ON SMOOTH SURFACES

Let X be a smooth projective surface such that linear and numerical equivalence of divisors on X coincide and let σ ⊆ |D| be a linear pencil on X with integral general fibers. A fiber of σ will be called special if either it is not integral or it has nongeneric multiplicity at some of the base points (including the infinitely near ones) of the pencil. In this paper, we provide a procedure to compute the integral components of the special fibers of σ.