We study the geometry underlying the difference between nonnegative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and quaternary quartics are shown to be ...

We introduce a notion of ampleness for subschemes of any codimension using the theory of q-ample line bundles. We also investigate certain geometric properties satisfied by ample subvarieties, e.g. the Lefschetz ...

We study the birational properties of hypersurfaces in products of projective spaces. In the case of hypersurfaces in Pm x Pn, we describe their nef, movable and e ective cones and determine when they are Mori dream ...