A fibration of ${mathbb R}^n$ by oriented copies of ${mathbb R}^p$ is called skew if no two fibers intersect nor contain parallel directions. Conditions on $p$ and $n$ for the existence of such a fibration were given by Ovsienko and Tabachnikov. A cl
assification of smooth fibrations of ${mathbb R}^3$ by skew oriented lines was given by Salvai, in analogue with the classification of oriented great circle fibrations of $S^3$ by Gluck and Warner. We show that Salvais classification has a topological variation which generalizes to characterize all continuous fibrations of ${mathbb R}^n$ by skew oriented copies of ${mathbb R}^p$. We show that the space of fibrations of ${mathbb R}^3$ by skew oriented lines deformation retracts to the subspace of Hopf fibrations, and therefore has the homotopy type of a pair of disjoint copies of $S^2$. We discuss skew fibrations in the complex and quaternionic setting and give a necessary condition for the existence of a fibration of ${mathbb C}^n$ (${mathbb H}^n$) by skew oriented copies of ${mathbb C}^p$ (${mathbb H}^p$).
We give explicit computational algorithms to construct minimal degree (always $le 4$) ramified covers of $Prj^1$ for algebraic curves of genus 5 and 6. This completes the work of Schicho and Sevilla (who dealt with the $g le 4$ case) on constructing
radical parametrisations of arbitrary genus $g$ curves. Zariski showed that this is impossible for the general curve of genus $ge 7$. We also construct minimal degree birational plane models and show how the existence of degree 6 plane models for genus 6 curves is related to the gonality and geometric type of a certain auxiliary surface.
In this paper we describe a generalisation and adaptation of Kedlayas algorithm for computing the zeta function of a hyperelliptic curve over a finite field of odd characteristic that the author used for the implementation of the algorithm in the Mag
ma library. We generalise the algorithm to the case of an even degree model. We also analyse the adaptation of working with the $x^idx/y^3$ rather than the $x^idx/y$ differential basis. This basis has the computational advantage of always leading to an integral transformation matrix whereas the latter fails to in small genus cases. There are some theoretical subtleties that arise in the even degree case where the two differential bases actually lead to different redundant eigenvalues that must be discarded.
