## Abstract

The Hilbert scheme of n points in the projective plane parameterizes degree n zerodimensional 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 on P^{N} is a vector bundle E admitting a resolution of the form 0→O_{PN} (-1)s M→Os+rP _{N} →E →0,where the map M is general. We complete the classification of slopes of semistable Steiner bundles on P_{N} by 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 on P^{1} which is interesting in its own right.

Original language | English (US) |
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Pages (from-to) | 4829-4873 |

Number of pages | 45 |

Journal | International Mathematics Research Notices |

Volume | 2013 |

Issue number | 21 |

DOIs | |

State | Published - Jan 1 2013 |

## All Science Journal Classification (ASJC) codes

- General Mathematics