Hilbert Scheme of a Pair of Codimension Two Linear Subspaces |
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| Authors: | Dawei Chen Izzet Coskun Scott Nollet |
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| Institution: | 1. Department of Mathematics, Statistics, and Computer Science , University of Illinois at Chicago , Chicago, Illinois, USA dwchen@math.uic.edu;3. Department of Mathematics, Statistics, and Computer Science , University of Illinois at Chicago , Chicago, Illinois, USA;4. Department of Mathematics , Texas Christian University , Fort Worth, Texas, USA |
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| Abstract: | We study the component H n of the Hilbert scheme whose general point parameterizes a pair of codimension two linear subspaces in ? n for n ≥ 3. We show that H n is smooth and isomorphic to the blow-up of the symmetric square of 𝔾(n ? 2, n) along the diagonal. Further H n intersects only one other component in the full Hilbert scheme, transversely. We determine the stable base locus decomposition of its effective cone and give modular interpretations of the corresponding models, hence conclude that H n is a Mori dream space. |
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| Keywords: | Hilbert scheme Mori dream space Stable base locus decomposition |
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