scholarly journals Hilbert schemes of points on some K3 surfaces and Gieseker stable bundles

1996 ◽  
Vol 120 (2) ◽  
pp. 255-261 ◽  
Author(s):  
Ugo Bruzzo ◽  
Antony Maciocia
Keyword(s):  
Moduli Spaces ◽  
Wide Class ◽  
Vector Bundles ◽  
K3 Surfaces ◽  
Hilbert Schemes ◽  
Stable Bundles ◽  
Stable Vector Bundles

AbstractBy using a Fourier-Mukai transform for sheaves on K3 surfaces we show that for a wide class of K3 surfaces X the Hilbert schemes Hilbn(X) can be identified for all n ≥ 1 with moduli spaces of Gieseker stable vector bundles on X. We also introduce a new Fourier-Mukai type transform for such surfaces.

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.

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.

scholarly journals Moduli spaces of the stable vector bundles over abelian surfaces

1980 ◽  
Vol 77 ◽  
pp. 47-60 ◽  
Author(s):  
Hiroshi Umemura
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Ample Line Bundle ◽  
Abelian Surfaces ◽  
Singular Variety ◽  
Stable Bundles ◽  
Stable Vector Bundles ◽  
Closed Subvariety

Let X be a projective non-singular variety and H an ample line bundle on X. The moduli space of H-stable vector bundles exists by Maruyama [4]. If X is a curve defined over C, the structure of the moduli space (or its compactification) M(X, d, r) of stable vector bundles of degree d and rank r on X is studied in detail. It is known that the variety M(X, d, r) is irreducible. Let L be a line bundle of degree d and let M(X, L, r) denote the closed subvariety of M(X, d, r) consisting of all the stable bundles E with det E = L.

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 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 Perverse bundles and Calogero–Moser spaces

2008 ◽  
Vol 144 (6) ◽  
pp. 1403-1428 ◽  
Author(s):  
David Ben-Zvi ◽  
Thomas Nevins
Keyword(s):  
Moduli Spaces ◽  
Vector Bundles ◽  
Hilbert Schemes ◽  
Simple Description ◽  
Quiver Varieties ◽  
Complex Curves ◽  
Noncommutative Version ◽  
Cotangent Bundles ◽  
Rank One ◽  
Torsion Free

AbstractWe present a simple description of moduli spaces of torsion-free 𝒟-modules (𝒟-bundles) on general smooth complex curves, generalizing the identification of the space of ideals in the Weyl algebra with Calogero–Moser quiver varieties. Namely, we show that the moduli of 𝒟-bundles form twisted cotangent bundles to moduli of torsion sheaves on X, answering a question of Ginzburg. The corresponding (untwisted) cotangent bundles are identified with moduli of perverse vector bundles on T*X, which contain as open subsets the moduli of framed torsion-free sheaves (the Hilbert schemes T*X[n] in the rank-one case). The proof is based on the description of the derived category of 𝒟-modules on X by a noncommutative version of the Beilinson transform on P1.

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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