Ample divisors on fine moduli spaces on the projective plane
type: Item
instance of: scholarly article
title: Ample divisors on fine moduli spaces on the projective plane
zbMATH Open document ID: 0533.14006
DOI: 10.1007/BF01161956
author: Stein Arild Strømme
published in: Mathematische Zeitschrift
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173500
review text: Let \(c_ 1\) and \(c_ 2\) be two integers with discriminant \(D=c_ 1\!^ 2-4c_ 2\) satisfying \(D<0\), \(D\neq -4\), and \(D\not\equiv 0(mod 8),\) and let \(M(c_ 1,c_ 2)\) be the fine moduli space for stable rank- 2 coherent sheaves on \({\mathbb{P}}^ 2\) with the given Chern classes. We prove that the Picard group of \(M(c_ 1,c_ 2)\) is free on two generators, and the geometric significance of these is given. The ample cone is described in terms of the generators. Furthermore, the divisor class of the non-locally free sheaves is computed, as well as the canonical class.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14D22
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 3845734
zbMATH Keywords: ample divisor
zbMATH Keywords: projective plane
zbMATH Keywords: fine moduli space for stable rank-2 coherent sheaves
zbMATH Keywords: Chern classes
zbMATH Keywords: Picard group
zbMATH Keywords: ample cone
MaRDI profile type: Publication
cites work: Moduli of vector bundles on the projective plane
cites work: Q3769024
cites work: On the moduli of vector bundles on an algebraic surface
cites work: Q4143433
cites work: Stable rank-2 vector bundles on \(\mathbb{P}_2\) with \(c_1\) odd
cites work: Q4187913
cites work: Fibres stables de rang 2 sur \(\mathbb{P}_2(\mathbb{C})\)
cites work: Sur le groupe de Picard de l'espace de modules des fibrés stables sur $\mathbb{P}_2$
cites work: Moduli of stable sheaves. II
cites work: Q5525818
cites work: Vector Bundles on Algebraic Surfaces
cites work: The Secant Bundle of a Projective Variety
OpenAlex ID: W67374011
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description: scientific article; zbMATH DE number 3845734