Hilbert Schemes of Points and Partially Ample Line Bundles
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Hilbert Schemes of Points and Partially Ample Line Bundles

  • Author(s): Khan, Mohammed Harris
  • Advisor(s): Totaro, Burt
  • et al.
Abstract

This dissertation has two parts. The first part computes the integral homology of theHilbert scheme of three points in affine n-space, as well as the Hilbert scheme of four points in affine n-space. It also provides partial results on the Hilbert scheme of five points in affine n-space. The second part deals with partially ample line bundles on projective schemes, and determines the shape of the cone corresponding to them. It verifies for several projective schemes the conjecture that the so called q-ample cone is the interior of the finite union of rational polyhedral cones.

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