We determine in an elementary fashion the dimension of the space of innni-tesimal deformations of an arbitrary vector bundle on the complex projective line, showing its dependence on the precise form of the decomposition of the bundle under consideration.

We investigate the deformations of pairs [Formula: see text], where text] is a line bundle on smooth projective variety defined over an algebraically closed field characteristic 0. In particular, we prove that DG-Lie algebra controlling pair homotopy abelian whenever has trivial canonical bundle, and so these are unobstructed.

Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular, we obtain a discrete analogue of a theorem of André Weil on the classificati...

Bundle methods have been used frequently to solve nonsmooth optimization problems. In these methods, subgradient directions from past iterations are accumulated in a bundle, and a trial direction is obtained by performing quadratic programming based on the information contained in the bundle. A line search is then performed along the trial direction, generating a serious step if the function va...

We prove that Oeljeklaus-Toma manifolds of simple type are rigid, and any line bundle on an manifold is flat.