The aim of this paper is to examine various interesting results from the theory of general cub~c curves in projective planes of characteristic two. This leads to calculations involving nets of conics in the plane, invariants of the curves, syzygies, and Hessians. It is emphasized that classical methods, (that is those developed for geometries over fields of zero characteristic), do not always s...

Introduction. In [Ge1] Gekeler classified all elliptic curves over F2r (T ) with one rational place of multiplicative reduction (without loss of generality located at ∞), one further rational place of bad reduction (without loss of generality located at 0) and good reduction elsewhere. So these curves have conductor ∞ · T where n is a natural number (which actually can be arbitrarily large). In...

Let k = Fq be a finite field of characteristic 2. A genus 3 curve C/k has many involutions if the group of k-automorphisms admits a C2 × C2 subgroup H (not containing the hyperelliptic involution if C is hyperelliptic). Then C is an ArtinSchreier cover of the three elliptic curves obtained as the quotient of C by the nontrivial involutions of H , and the Jacobian of C is k-isogenous to the prod...

This paper presents a novel surface modelling scheme to construct a freeform surface progressively from unorganised curves representing the boundary and interior characteristic curves. The approach can construct a base surface model from four ordinary or composite boundary curves and support incremental surface updating from interior characteristic curves, some of which may not be on the final ...

Let k be a global field of positive characteristic, and let σ : X −→ Spec k be a smooth projective curve. We study the zero-dimensional cycle group V (X) = Ker(σ∗ : SK1(X) → K1(k)) and the one-dimensional cycle group W (X) = coker(σ∗ : K2(k) → H0 Zar(X,K2)), addressing the conjecture that V (X) is torsion and W (X) is finitely generated. The main idea is to use Abhyankar’s Theorem on resolution...

We study the automorphism groups of the reduction X0(N)× F̄p of a modular curve X0(N) over primes p ∤ N .

A curve over finite field is supersingular if its Jacobian is supersingular as an abelian variety. On the one hand, supersingular abelian varieties form the smallest (closed) stratum in the moduli space of abelian varieties, on the other the intersection of Jacobian locus and the stratification of moduli space is little known. Consequently it is very difficult to locate a family of supersingula...

Here we study (in positive characteristic) integral curves X ⊂ Pr with secant degree one, i.e., for which a general P ∈ Seck−1(X) is in a unique k-secant (k − 1)-dimensional linear subspace.

Receiver operating characteristic (ROC) curves are frequently used to compare the accuracy of two or more imaging modalities. This paper addresses the use of ROC analysis to evaluate the speed and accuracy of digital mammography, as compared to conventional film-screen mammography.

Receiver operating characteristic (ROC) curves are frequently used in biomedical informatics research to evaluate classification and prediction models for decision support, diagnosis, and prognosis. ROC analysis investigates the accuracy of a model's ability to separate positive from negative cases (such as predicting the presence or absence of disease), and the results are independent of the p...