Moduli spaces of stable rank-2 bundles on ruled surfaces

1992 ◽  
Vol 110 (1) ◽  
pp. 615-626 ◽  
Author(s):  
Zhenbo Qin
Keyword(s):  
Moduli Spaces ◽  
Stable Rank ◽  
Ruled Surfaces ◽  
Rank 2 ◽  
Rank 2 Bundles

STABLE RANK-2 BUNDLES ON CALABI–YAU MANIFOLDS

2003 ◽  
Vol 14 (10) ◽  
pp. 1097-1120 ◽  
Author(s):  
WEI-PING LI ◽  
ZHENBO QIN
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Double Cover ◽  
Stable Rank ◽  
Chern Classes ◽  
Canonical Divisor ◽  
Rank 2 ◽  
Stable Sheaves ◽  
Rank 2 Bundles ◽  
Calabi Yau Manifolds

In this paper, we apply the technique of chamber structures of stability polarizations to construct the full moduli space of rank-2 stable sheaves with certain Chern classes on Calabi–Yau manifolds which are anti-canonical divisor of ℙ1×ℙn or a double cover of ℙ1×ℙn. These moduli spaces are isomorphic to projective spaces. As an application, we compute the holomorphic Casson invariants defined by Donaldson and Thomas.

scholarly journals Finding ein components in the moduli spaces of stable rank 2 bundles on the projective 3-space

2016 ◽  
Vol 57 (2) ◽  
pp. 322-329 ◽  
Author(s):  
A. A. Kytmanov ◽  
N. N. Osipov ◽  
S. A. Tikhomirov
Keyword(s):  
Moduli Spaces ◽  
Stable Rank ◽  
Rank 2 ◽  
Rank 2 Bundles

scholarly journals Construction of Stable Rank 2 Bundles on ℙ3 Via Symplectic Bundles

2019 ◽  
Vol 60 (2) ◽  
pp. 343-358 ◽  
Author(s):  
A. S. Tikhomirov ◽  
S. A. Tikhomirov ◽  
D. A. Vassiliev
Keyword(s):  
Stable Rank ◽  
Rank 2 ◽  
Rank 2 Bundles

Restriction of Stable Bundles on an Abelian Surface. The C2 = 2 Case

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Cristian Anghel
Keyword(s):  
Moduli Space ◽  
Stable Rank ◽  
Abelian Surface ◽  
Restriction Map ◽  
Stable Bundles ◽  
Genus 2 ◽  
Rank 2 ◽  
Dimension 2 ◽  
Rank 2 Bundles

Abstract In this note we describe the restriction map from the moduli space of stable rank 2 bundles with c2 = 2 on a jacobian X of dimension 2, to the moduli space of stable rank 2 bundles on the corresponding genus 2 curve C embedded in X.

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 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.

Sign in / Sign up

Export Citation Format

Share Document