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The Hilbert scheme of  n  points in the projective plane parameterizes degree  n  zero-dimensional subschemes of the projective plane. We examine the dual cones of effective divisors and moving curves on the Hilbert scheme. By studying interpolation, restriction, and stability properties of certain vector bundles on the plane, we fully determine these cones for just over three-fourths of all values of  n . A  general Steiner bundle  onis a vector bundle  E  admitting a resolution of the formwhere the map  M  is general. We complete the classification of slopes of semistable Steiner bundles onby showing every admissible slope is realized by a bundle which restricts itself to a balanced bundle on a rational curve. The proof involves a basic question about multiplication of polynomials onwhich is interesting in its own right.

Restrictions of Steiner Bundles and Divisors on the Hilbert Scheme of Points in the Plane