scholarly journals Reducibility of the Moduli Space of Stable Rank 2 Reflexive Sheaves with Chern Classes c1 = −1, c2 = 4, c3 = 2 on Projective Space P³

2014 ◽  
Vol 21 (2) ◽  
pp. 90-96
Author(s):  
A. S. Tikhomirov ◽  
M. A. Zavodchikov
Keyword(s):  
Projective Space ◽  
Moduli Space ◽  
Stable Rank ◽  
Chern Classes ◽  
Rank 2

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 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.

ON SINGULARITIES OF ℳℙ3 (c1, c2)

1998 ◽  
Vol 09 (04) ◽  
pp. 407-419 ◽  
Author(s):  
VINCENZO ANCONA ◽  
GIORGIO OTTAVIANI
Keyword(s):  
Moduli Space ◽  
Vector Bundles ◽  
Stable Rank ◽  
Chern Classes ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

Let ℳℙ3(c1,c2) be the moduli space of stable rank-2 vector bundles on ℙ3 with Chern classes c1, c2. We prove the following results: (1) Let k, β, γ be three integers such that k > 0, 0 ≤ β < γ, γ ≥ 2, kγ - (k + 1)β > 0; then the moduli space ℳℙ3(0, kγ2 - (k + 1)β2) is singular (the case k = 2, β = 0 was previously proved by M. Maggesi). (2) Let k, β, γ be three integers, with β and γ odd, such that k > 0, 0 < β < γ, γ ≥ 5, kγ - (k + 1)β + 1 > 0; then the moduli space ℳℙ3(-1,k(γ/2)2 - (k + 1)(β/2)2) + 1/4) is singular. In particular ℳℙ3(0,5), ℳℙ3(-1,6) are singular.

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 On the Connectedness of the Real Part of Moduli Spaces of Vector Bundles on Real Algebraic Surfaces

2000 ◽  
Vol 68 (1) ◽  
pp. 41-54
Author(s):  
Edoardo Ballico
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Algebraic Surfaces ◽  
Stable Rank ◽  
Projective Surface ◽  
Chern Classes ◽  
The Real ◽  
Smooth Projective Surface ◽  
Real Algebraic Surfaces

AbstractLet X be a smooth projective surface with q(X) = 0 defined over R and M(X;r;c1;c2;H) the moduli space of H-stable rank r vector bundles on X with Chern classes c1 and c2. Assume either r = 3 and X(R) connected or r = 3 and X(R) =ø or r=2 and X(R) = ø. We prove that quite often M is connected.

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).

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