Stably irrational hypersurfaces of small slopes

Digital lines with irrational slopes

How to construct a digitization of a straight line and be able to recognize a straight line in a set of pixels are very important topics in computer graphics. The aim of the present paper is to give a mathematically exact and consistent description of digital straight lines according to Rosenfeld’s definition. The digitizations of the lines with slopes 0 < a < 1, where a is irrational, are cons...

Hypersurfaces that are not stably rational

A fundamental problem of algebraic geometry is to determine which varieties are rational, that is, isomorphic to projective space after removing lower-dimensional subvarieties from both sides. In particular, we want to know which smooth hypersurfaces in projective space are rational. An easy case is that smooth complex hypersurfaces of degree at least n + 2 in P are not covered by rational curv...

A Run-hierarchical Description of Upper Mechanical Words with Irrational Slopes Using Continued Fractions

The main result is a run-hierarchical description (by continued fractions) of upper mechanical words with slope a ∈ ]0, 1[ \Q and intercept 0. We compare this description with two classical methods of forming of such words. In order to be able to perform the comparison, we present a quantitative analysis of our method. We use the denominators of the convergents of the continued fraction expansi...

Hopf Hypersurfaces of Small Hopf Principal Curvature in Ch

Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex hyperbolic space CH with any specified value of the Hopf principal curvature α less than or equal to the corresponding value for the horosphere. We give a construction for all such hypersurfaces in terms of Weierstrass-type data, and also obtain a classification of pseudo...

stably silencing of cd81 expression by small interfering rnas targeting 3&apos;-ntr inhibits hcv infection