Rank 2 stable vector bundles on \({\mathbb{P}}^ 3({\mathbb{C}})\) with Chern classes \(c_ 1=-1,\) \(c_ 2=4\)
type: Item
instance of: scholarly article
title: Rank 2 stable vector bundles on \({\mathbb{P}}^ 3({\mathbb{C}})\) with Chern classes \(c_ 1=-1,\) \(c_ 2=4\)
zbMATH Open document ID: 0566.14010
DOI: 10.1007/BF01215133
author: Constantin Bănică
author: Nicolae Manolache
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
review text: In this paper one shows that the moduli space M(-1,4) of stable rank 2 vector bundles on \({\mathbb{P}}^ 3\) with \(c_ 1=-1\), \(c_ 2=4\) has two connected components, corresponding to the two possible spectra: (-2,- 1,0,1),(-1,-1,0,0). Both of them are quasiprojective, irreducible, rational (of dimensions 27 and 28). The first is smooth, the other is showed to be generically smooth (the authors do not know whether it is also everywhere smooth). The method is to study the curves which are zero-sets of sections of E(t), E in M(-1,4), with t minimal. The paragraph 5 is probably of interest in itself, where an insight into the classification of curves of degree 6 (with nilpotents) is given.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 14D20
zbMATH DE Number: 3902807
zbMATH Keywords: Chern class
zbMATH Keywords: moduli space
zbMATH Keywords: stable rank 2 vector bundles
zbMATH Keywords: classification of curves of degree 6
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3902807