Corpus ID: 14506009

# On Stable Bundles of Ranks 2 and 3 on P^3

@article{Vitter2003OnSB,
title={On Stable Bundles of Ranks 2 and 3 on P^3},
author={A. Vitter},
journal={arXiv: Algebraic Geometry},
year={2003}
}
• A. Vitter
• Published 6 October 2003
• Mathematics
• arXiv: Algebraic Geometry
We study rank 3 stable bundles E on P^3 as extensions of a line bundle B on a smooth surface S in P^3 by the direct sum of three copies of O_{P^3}(-\nu). In most cases, S (the dependency locus of three sections of E(\nu)) lies in the Noether-Lefschetz locus. We give a detailed analysis when S contains a line L and B is constructed from divisors of the form aL+bC for H=L+C a hyperplane section of S. We study the parameter space of this construction and compare it to the full (Gieseker-Maruyama… Expand
1 Citations
Stable Vector Bundles as Generators of the Chow Ring
In this paper we show that the family of stable vector bundles gives a set of generators for the Chow ring, the K-theory and the derived category of any smooth projective variety.

#### References

SHOWING 1-10 OF 27 REFERENCES
Moduli of high rank vector bundles over surfaces
• Mathematics
• 1994
The purpose of this work is to apply the degeneration theory developed in [GL] to study the moduli space of stable vector bundles of arbitrary rank on any smooth algebraic surface (over C). We willExpand
Moduli of vector bundles on projective surfaces: some basic results
We prove that moduli spaces of torsion-free sheaves on a projective smooth complex surface are irreducible, reduced and of the expected dimension, provided the expected dimension is large enough.Expand
Lectures on Vector Bundles
Part I. Vector Bundles On Algebraic Curves: 1. Generalities 2. The Riemann-Roch formula 3. Topological 4. The Hilbert scheme 5. Semi-stability 6. Invariant geometry 7. The construction of M(r,d) 8.Expand
On the Noether-Lefschetz theorem and some remarks on codimension-two cycles
• Mathematics
• 1985
Here, "of general moduli" means that there is a countable union V of subvarieties of the space pN of surfaces of degree d in p3, such that the statement Pie(S) = Z holds for S ~ p N _ V. Noether, itExpand
Algebraic Surfaces and Holomorphic Vector Bundles
1 Curves on a Surface.- Invariants of a surface.- Divisors on a surface.- Adjunction and arithmetic genus.- The Riemann-Roch formula.- Algebraic proof of the Hodge index theorem.- Ample and nefExpand
The geometry of moduli spaces of sheaves
• Mathematics
• 1997
Preface to the second edition Preface to the first edition Introduction Part I. General Theory: 1. Preliminaries 2. Families of sheaves 3. The Grauert-Mullich Theorem 4. Moduli spaces Part II.Expand
A connectedness theorem for projective varieties, with applications to intersections and singularities of mappings
• Mathematics
• 1979
1. Summary A general connectedness theorem is proved, which implies several surprising but basic facts about projective varieties. Unless otherwise indicated, varieties will be complete, but possiblyExpand
On the zeta function of a hypersurface
Abstract : This article is concerned with the further development of the methods of p-adic analysis used in an earlier article to study the zeta function of an algebraic variety defined over a finiteExpand
Moduli of representations of the fundamental group of a smooth projective variety. II
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