An algebraic fibre bundle over P1 that is not a vector bundle

Universal Vector Bundle over the Reals

Let XR be a geometrically irreducible smooth projective curve, defined over R, such that XR does not have any real points. Let X = XR×R C be the complex curve. We show that there is a universal real algebraic line bundle over XR × Pic d(XR) if and only if χ(L) is odd for L ∈ Picd(XR). There is a universal quaternionic algebraic line bundle over X × Pic(X) if and only if the degree d is odd. Tak...

To bundle or not to bundle

Commodity bundling is studied in an environment where the dispersion of valuations unambiguously decreases when two or more goods are sold as a bundle only. Bundling is more likely to dominate separately selling the goods if marginal costs are low relative to the average valuation, or if the distribution of valuations is very peaked around the mean. ∗This note unbundles results previously provi...

Criticality in a Fibre - Bundle type model

The dynamics of a fibre-bundle type model with equal load sharing rule is numerically studied. The system, formed by N elements, is driven by a slow increase of the load upon it which is removed in a novel way through internal transfers to the elements broken during avalanches. When an avalanche ends, failed elements are regenerated with strengths taken from a probability distribution. For a la...

Supermanifolds Corresponding to the Trivial Vector Bundle over Complex Torus

Fibre bundle formulation of relativistic quantum mechanics

We propose a new fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in different directions. In the bundle description the wavefunctions are replaced with (state) sections (covariant approach) or liftings of paths (equivalently: s...