Die Modulräume \(^3M^{st}_{{\mathbb{P}}^3}(-2,3,c_3)\) (Q762572)
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scientific article; zbMATH DE number 3889703
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Die Modulräume \(^3M^{st}_{{\mathbb{P}}^3}(-2,3,c_3)\) |
scientific article; zbMATH DE number 3889703 |
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Die Modulräume \(^3M^{st}_{{\mathbb{P}}^3}(-2,3,c_3)\) (English)
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1984
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Let M(n) be the moduli space for stable reflexive rank-3 sheaves on \({\mathbb{P}}^ 3\) with \(c_ 1=-2,\quad c_ 2=3,\) and \(c_ 3=n.\) The theorem proved in this paper is: If \(n=-4,-2, 0,\quad or\quad 2,\) then M(n) is irreducible and smooth of dimension 12 (for other values of n it is empty). If \(n=-2\) or \(+2\), then M(n) is rational. - The following techniques are used in the proof: Spectrum, ''reduction step'', Beilinson spectral sequence, monads, and deformation theory.
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moduli space for stable reflexive rank-3 sheaves
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Spectrum
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reduction step
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monads
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deformation theory
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