# 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} }

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

#### One Citation

Stable Vector Bundles as Generators of the Chow Ring

- Mathematics
- 2003

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 will… Expand

Moduli of vector bundles on projective surfaces: some basic results

- Mathematics
- 1994

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

- Mathematics
- 1997

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, it… Expand

Algebraic Surfaces and Holomorphic Vector Bundles

- Mathematics
- 1998

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 nef… Expand

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 possibly… Expand

On the zeta function of a hypersurface

- Mathematics
- 1962

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 finite… Expand

Moduli of representations of the fundamental group of a smooth projective variety. II

- Mathematics
- 1994

© Publications mathématiques de l’I.H.É.S., 1994, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://… Expand