Die Modulräume \(^3M^{st}_{{\mathbb{P}}^3}(-2,3,c_3)\)
type: Item
instance of: scholarly article
title: Die Modulräume \(^3M^{st}_{{\mathbb{P}}^3}(-2,3,c_3)\)
zbMATH Open document ID: 0558.14016
DOI: 10.1007/BF01456095
author: Christian Okonek
author: Heinz Spindler
published in: Mathematische Annalen
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163899
review text: 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.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 14D20
zbMATH DE Number: 3889703
zbMATH Keywords: moduli space for stable reflexive rank-3 sheaves
zbMATH Keywords: Spectrum
zbMATH Keywords: reduction step
zbMATH Keywords: monads
zbMATH Keywords: deformation theory
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3889703