scholarly journals The moduli space of stable vector bundles over a real algebraic curve

2009 ◽  
Vol 347 (1) ◽  
pp. 201-233 ◽  
Author(s):  
Indranil Biswas ◽  
Johannes Huisman ◽  
Jacques Hurtubise
Keyword(s):  
Moduli Space ◽  
Algebraic Curve ◽  
Vector Bundles ◽  
Stable Vector Bundles ◽  
Real Algebraic Curve

scholarly journals EXTENSIONS AND RANK-2 VECTOR BUNDLES ON IRREDUCIBLE NODAL CURVES

2005 ◽  
Vol 16 (10) ◽  
pp. 1081-1118
Author(s):  
D. ARCARA
Keyword(s):  
Moduli Space ◽  
Vector Bundles ◽  
Rational Map ◽  
Nodal Curves ◽  
Nodal Curve ◽  
Stable Vector Bundles ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

We generalize Bertram's work on rank two vector bundles to an irreducible projective nodal curve C. We use the natural rational map [Formula: see text] defined by [Formula: see text] to study a compactification [Formula: see text] of the moduli space [Formula: see text] of semi-stable vector bundles of rank 2 and determinant L on C. In particular, we resolve the indeterminancy of ϕL in the case deg L = 3,4 via a sequence of three blow-ups with smooth centers.

scholarly journals Moduli spaces of orthogonal and symplectic bundles over an algebraic curve

2008 ◽  
Vol 144 (3) ◽  
pp. 721-733 ◽  
Author(s):  
Olivier Serman
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Algebraic Curve ◽  
Vector Bundles ◽  
Explicit Description ◽  
Representation Space ◽  
Classical Groups ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
Polynomial Invariants

AbstractWe prove that, given a smooth projective curve C of genus g≥2, the forgetful morphism $\mathcal {M}_{\mathbf {O}_r} \longrightarrow \mathcal {M}_{\mathbf {GL}_r}$ (respectively $\mathcal M_{\mathbf {Sp}_{2r}}\longrightarrow \mathcal M_{\mathbf {GL}_{2r}}$) from the moduli space of orthogonal (respectively symplectic) bundles to the moduli space of all vector bundles over C is an embedding. Our proof relies on an explicit description of a set of generators for the polynomial invariants on the representation space of a quiver under the action of a product of classical groups.

scholarly journals Moduli spaces of stable vector bundles on Enriques surfaces

1998 ◽  
Vol 150 ◽  
pp. 85-94 ◽  
Author(s):  
Hoil Kim
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
K3 Surface ◽  
Enriques Surface ◽  
Stable Bundles ◽  
Stable Vector Bundles ◽  
Enriques Surfaces

Abstract.We show that the image of the moduli space of stable bundles on an Enriques surface by the pull back map is a Lagrangian subvariety in the moduli space of stable bundles, which is a symplectic variety, on the covering K3 surface. We also describe singularities and some other features of it.

Moduli of Rank 2 Stable Bundles and Hecke Curves

2016 ◽  
Vol 59 (4) ◽  
pp. 865-877
Author(s):  
Sarbeswar Pal
Keyword(s):  
Moduli Space ◽  
Vector Bundles ◽  
Short Note ◽  
Equivalence Classes ◽  
Complex Numbers ◽  
Stable Bundles ◽  
Smooth Projective Curve ◽  
Stable Vector Bundles ◽  
Arbitrary Genus ◽  
Rank 2

AbstractLet X be a smooth projective curve of arbitrary genus g > 3 over the complex numbers. In this short note we will show that the moduli space of rank 2 stable vector bundles with determinant isomorphic to Lx , where Lx denotes the line bundle corresponding to a point x ∊ X, is isomorphic to a certain variety of lines in the moduli space of S-equivalence classes of semistable bundles of rank 2 with trivial determinant.

scholarly journals Stability of some vector bundles on Hilbert schemes of points on K3 surfaces

2021 ◽  
Author(s):  
Fabian Reede ◽  
Ziyu Zhang
Keyword(s):  
Moduli Space ◽  
Hilbert Scheme ◽  
Vector Bundles ◽  
K3 Surfaces ◽  
Hilbert Schemes ◽  
Connected Component ◽  
Stable Vector Bundles ◽  
Universal Family ◽  
Hilbert Scheme Of Points ◽  
Flat Family

AbstractLet X be a projective K3 surfaces. In two examples where there exists a fine moduli space M of stable vector bundles on X, isomorphic to a Hilbert scheme of points, we prove that the universal family $${\mathcal {E}}$$ E on $$X\times M$$ X × M can be understood as a complete flat family of stable vector bundles on M parametrized by X, which identifies X with a smooth connected component of some moduli space of stable sheaves on M.

On the Image of Certain Extension Maps. I

2007 ◽  
Vol 50 (3) ◽  
pp. 427-433
Author(s):  
Israel Moreno Mejía
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
Vector Bundles ◽  
Projective Curve ◽  
Rational Map ◽  
Stable Vector Bundles ◽  
Linear Subspaces ◽  
Smooth Complex ◽  
Complex Projective ◽  
Complex Projective Curve

AbstractLet X be a smooth complex projective curve of genus g ≥ 1. Let ξ ∈ J1(X) be a line bundle on X of degree 1. LetW = Ext1(ξn, ξ–1) be the space of extensions of ξn by ξ–1. There is a rational map Dξ : G(n,W) → SUX(n + 1), where G(n,W) is the Grassmannian variety of n-linear subspaces of W and SUX(n + 1) is the moduli space of rank n + 1 semi-stable vector bundles on X with trivial determinant. We prove that if n = 2, then Dξ is everywhere defined and is injective.

scholarly journals CHEN–RUAN COHOMOLOGY OF SOME MODULI SPACES, II

2010 ◽  
Vol 21 (04) ◽  
pp. 497-522 ◽  
Author(s):  
INDRANIL BISWAS ◽  
MAINAK PODDAR
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Prime Number ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Line Bundles ◽  
Holomorphic Line Bundle ◽  
Stable Vector Bundles

Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and ξ → X a holomorphic line bundle such that r is not a divisor of degree ξ. Let [Formula: see text] denote the moduli space of stable vector bundles over X of rank r and determinant ξ. By Γ we will denote the group of line bundles L over X such that L⊗r is trivial. This group Γ acts on [Formula: see text] by the rule (E, L) ↦ E ⊗ L. We compute the Chen–Ruan cohomology of the corresponding orbifold.

scholarly journals Rationality of moduli spaces of vector bundles on rational surfaces

2002 ◽  
Vol 165 ◽  
pp. 43-69 ◽  
Author(s):  
Laura Costa ◽  
Rosa M. Miro-Ŕoig
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Rational Surface ◽  
Rational Surfaces ◽  
Stable Vector Bundles

Let X be a smooth rational surface. In this paper, we prove the rationality of the moduli space MX,L(2; c1; c2) of rank two L-stable vector bundles E on X with det (E) = c1 ∈ Pic(X) and c2(E) = c2 ≫ 0.

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