Stable rank 2 vector bundles with Chern-classesc 1=?1,c 2=4

1986 ◽  
Vol 275 (3) ◽  
pp. 481-500 ◽  
Author(s):  
Wolfram Decker
Keyword(s):  
Vector Bundles ◽  
Stable Rank ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

Maximal Subbundles of Rank 2 Vector Bundles on Projective Curves

2000 ◽  
Vol 43 (2) ◽  
pp. 129-137 ◽  
Author(s):  
E. Ballico
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Stable Rank ◽  
Maximal Degree ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
Stable Vector Bundles ◽  
Projective Curves ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

AbstractLet E be a stable rank 2 vector bundle on a smooth projective curve X and V(E) be the set of all rank 1 subbundles of E with maximal degree. Here we study the varieties (non-emptyness, irreducibility and dimension) of all rank 2 stable vector bundles, E, on X with fixed deg(E) and deg(L), L ∈ V(E) and such that .

Stable rank-2 vector bundles on ?2119;2 withc 1 odd

1979 ◽  
Vol 242 (3) ◽  
pp. 241-266 ◽  
Author(s):  
Klaus Hulek
Keyword(s):  
Vector Bundles ◽  
Stable Rank ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

scholarly journals The moduli of a class of rank 2 vector bundles on P3

1981 ◽  
Vol 84 ◽  
pp. 9-30 ◽  
Author(s):  
G. Pete Wever
Keyword(s):  
Projective Space ◽  
Vector Bundles ◽  
Finite Union ◽  
Stable Rank ◽  
Projective Varieties ◽  
Algebraic Vector ◽  
Rank 2 ◽  
Rank 2 Vector Bundles ◽  
Rank 2 Bundles

Barth and others [1], [2], [5] have begun the study of stable algebraic vector bundles of rank 2 on projective space. Maruyama [7] has shown that stable rank 2 bundles have a variety of moduli which is the finite union of quasi-projective varieties.

scholarly journals The wobbly divisors of the moduli space of rank-2 vector bundles

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sarbeswar Pal ◽  
Christian Pauly
Keyword(s):  
Moduli Space ◽  
Vector Bundles ◽  
Higgs Field ◽  
Picard Group ◽  
Stable Rank ◽  
Complex Curve ◽  
Stable Vector Bundles ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

Abstract Let X be a smooth projective complex curve of genus g ≥ 2 and let M X (2,Λ) be the moduli space of semi-stable rank-2 vector bundles over X with fixed determinant Λ. We show that the wobbly locus, i.e. the locus of semi-stable vector bundles admitting a non-zero nilpotent Higgs field, is a union of divisors 𝓦 k ⊂ M X (2,Λ). We show that on one wobbly divisor the set of maximal subbundles is degenerate. We also compute the class of the divisors 𝓦 k in the Picard group of M X (2, Λ).

scholarly journals Stable vector bundles on quadric hypersurfaces

1984 ◽  
Vol 96 ◽  
pp. 11-22 ◽  
Author(s):  
L. Ein ◽  
I. Sols
Keyword(s):  
Vector Bundles ◽  
Stable Rank ◽  
Vanishing Theorem ◽  
Restriction Theorem ◽  
Stable Vector Bundles ◽  
Rational Varieties ◽  
Rank 2 ◽  
Rank 2 Vector Bundles ◽  
Definition Of ◽  
Rank 2 Bundles

Barth, Hulek and Maruyama have showed that the moduli of stable rank 2 vector bundles on P2 are nonsingular rational varieties. There are also many examples of stable rank 2 vector bundles on P3. On the other hand, there is essentially only one example of rank 2 bundles on P4, which is constructed by Horrocks and Mumford. We hope the study of rank 2 bundles on hypersurfaces in P4 may give more insight to the study of vector bundles on P4. In this paper, we establish some general properties of stable rank 2 bundles on quadric hypersurfaces. We show the restriction theorem (1.4), (1.6), the existence of the spectrum (2.2), and the vanishing theorem (2.4), are also true for the stable rank 2 reflexive sheaves on quadric hypersurfaces just as in the case when the base variety is Pn. Though the methods to prove such results are similar to those we use for projective spaces, there are some technical difficulties. We should also mention that we shall always assume the base field is characteristic 0 and algebraically closed, and we shall use the definition of stability introduced by Mumford and Takemoto.

scholarly journals The Mercat Conjecture for stable rank 2 vector bundles on generic curves

2018 ◽  
Vol 140 (5) ◽  
pp. 1277-1295 ◽  
Author(s):  
Benjamin Bakker ◽  
Gavril Farkas
Keyword(s):  
Vector Bundles ◽  
Stable Rank ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

scholarly journals Generalized null correlation bundles

1988 ◽  
Vol 111 ◽  
pp. 13-24 ◽  
Author(s):  
Lawrence Ein
Keyword(s):  
Moduli Space ◽  
Vector Bundles ◽  
Topological Type ◽  
Stable Rank ◽  
Chern Classes ◽  
Smooth Variety ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

It is well known that the moduli space of stable rank 2 vector bundles on ℙ2 of the fixed topological type is an irreducible smooth variety ([1], and [8]). There are also many known results on the classification of stable rank 2 vector bundles on ℙ3 with “small” Chern classes.

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