We give counterexamples to the Kawamata-Viehweg vanishing theorem on ruled surfaces in positive characteristic, and prove that if there is a counterexample to the Kawamata-Viehweg vanishing theorem on a geometrically ruled surface f : X → C, then either C is a Tango curve or all of sections of f are ample.

To each del Pezzo surface Xn (resp. ruled surface, ruled surface with a section), we describe a natural Lie algebra bundle of type En (resp. Dn−1, An−2) over it . Using lines and rulings on any such surface, we describe various representation bundles corresponding to fundamental representations of the corresponding Lie algebra. When we specify a geometric structure on the surface to reduce the ...

We show that hyperelliptic symplectic Lefschetz fibrations are symplectically birational to two-fold covers of rational ruled surfaces, branched in a symplectically embedded surface. This reduces the classification of genus 2 fibrations to the classification of certain symplectic submanifolds in rational ruled surfaces.

Solar energy is a new renewable energy. Using solar to generate electricity an effective means achieve sustainable development. The huge roof at the top of airport natural interface receive energy, which can be used supply needed by through building integrated photovoltaic design. However, due curved shape roof, there are limitations in acquisition and construction roof. In this paper, method “...

We prove an existence result for stable vector bundles with arbitrary rank on an algebraic surface, and determine the birational structure of certain moduli space of stable bundles on a rational ruled surface.

Ruled surface design and its applications are widely used in CAGD (Computer Aided Geometric Design) and industrial areas. The hyperbolic paraboloid, the cylinder, the cone, and the hyperboloid are ruled surfaces with particular shapes. In this paper, dual space drawing methods for these particular ruled surfaces are proposed. The underlying principles of these methods are the applications, exte...