Complex projective elliptic surfaces endowed with a numerically effective line bundle of arithmetic genus two are studied and partially classified. A key role is played by elliptic quasi-bundles, where some ideas developed by Serrano in order to study ample line bundles apply to this more general situation.
Given a compact affine nonsingular real algebraic variety X and a nonsingular subvariety Z C X belonging to a large class of subvarieties, we show how to embed X in a suitable Grassmannian so that Z becomes the transverse intersection of the zeros of a section of the tautological bundle on the Grassmannian.
We consider the family of polynomials in of the form . Two such polynomials and are equivalent if there is an automorphism of such that . We give a complete classification of the equivalence classes of these polynomials in the algebraic and analytic category. As a consequence, we find the following results. There are explicit examples of inequivalent polynomials and such that the zero set of is isomorphic to the zero set of for all . There exist polynomials which are algebraically...