Affine surfaces fibered by affine lines over the projective line

Torsors over the Punctured Affine Line

We classify G-torsors over the punctured affine line Spec (k[t]) where G is a reductive algebraic group defined over a field k of good characteristic. Our classification is in terms of the Galois cohomology of the complete field k((t)) with values in G.

Affine and projective planes

Uncalibrated 1D projective camera and 3D affine reconstruction of lines

We describe a linear algorithm to recover 3D affine shape/motion from line correspondences over three views with uncalibrated affine cameras. The key idea is the introduction of a one-dimensional projective camera. This converts the 3D affine reconstruction of “lines” into 2D projective reconstruction of “points”. Using the full tensorial representation of three uncalibrated 1D views, we prove ...

Affine and Projective Universal Geometry

By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are introduced here, and the main formulas extend those of rational trigonometry in the plane. This gives a unified, computational model of both spherical and hyp...

Affine Spaces within Projective Spaces

We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our concepts to the problem of describing dual spreads. We do not assume that the projective space is finitedimensional or pappian. Mathematics Subject Classification...