Characteristic curves like isophotes, reflection lines and reflection circles are well–established concepts which have been used for automatic fairing of both parametric and piecewise linear surfaces. However, the result of the fairing strongly depends on the choice of a particular family of characteristic curves: isophotes or reflection lines may look perfect for a certain orientation of viewi...

We give a geometric approach to the relation between the irreducible components of the characteristic varieties of local systems on a plane curve arrangement complement and the associated pencils of plane curves discovered recently by M. Falk and S. Yuzvinsky [10] in the case of line arrangements. In this case, this geometric point of view was already hinted to by A. Libgober and S. Yuzvinsky, ...

The classi cation of foliated surfaces, [McQ08], is applied to the study of curves on surfaces with big co-tangent bundle and varying moduli, be it purely in characteristic zero, or, more generally when the characteristic is mixed. Almost everything that one might naively imagine is true, but with one critical exception: rational curves on bi-disc quotients which aren't quotients of products of...

The genus g of an Fq2-maximal curve satisfies g = g1 := q(q − 1)/2 or g ≤ g2 := ⌊(q − 1) /4⌊. Previously, Fq2 -maximal curves with g = g1 or g = g2, q odd, have been characterized up to Fq2 -isomorphism. Here it is shown that an Fq2 -maximal curve with genus g2, q even, is Fq2 -isomorphic to the nonsingular model of the plane curve ∑t i=1 y q/2 = x, q = 2, provided that q/2 is a Weierstrass non...

Let k be an algebraically closed field of characteristic p. Let X(p;N) be the curve parameterizing elliptic curves with full level N structure (where p N) and full level p Igusa structure. By modular curve, we mean a quotient of any X(p;N) by any subgroup of ((Z/peZ)× × SL2(Z/NZ)) /{±1}. We prove that in any sequence of distinct modular curves over k, the k-gonality tends to infinity. This exte...

Let α be an automorphism of a hyperelliptic curve C of genus g and let α be the automorphism induced by α on the genus-0 quotient of C by the hyperelliptic involution. Let n be the order of α and let n be the order of α. We show that the characteristic polynomial f of the automorphism α∗ of the Jacobian of C is determined by the values of n, n, and g, unless n = n, n is even, and (2g + 2)/n is ...

nalyzing and interrogating designed surfaces remains an important and widely researched issue in computer-aided geometric design (CAGD). Treating families of characteristic curves— such as contour lines, lines of curvature, asymptotic lines, isophotes, and reflection lines—on the surface proves a popular method of doing this. All these curves have something in common: s They reflect the surface...

In this issue of the Journal, Auer and colleagues conclude that serum levels of neuron-specific enolase (NSE), a biochemical marker of ischemic brain injury, may have clinical utility for the prediction of survival to hospital discharge in patients experiencing the return of spontaneous circulation following at least 5 minutes of cardiopulmonary resuscitation. The authors used a receiver operat...

This review introduces some commonly used methods for assessing the performance of a diagnostic test. The sensitivity, specificity and likelihood ratio of a test are discussed. The uses of the receiver operating characteristic curve and the area under the curve are explained.