A new six-dimensional irreducible symplectic variety

DOI10.1090/S1056-3911-03-00323-0zbMath1068.53058arXivmath/0010187OpenAlexW2141299286MaRDI QIDQ4461665

Kieran G. O'Grady

Publication date: 18 May 2004

Published in: Journal of Algebraic Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0010187

zbMATH Keywords

moduli spaceHilbert schemehyper-KählerMukai vectorholomorphic symplectic formBogomolov decomposition.Ricci flat Kähler metric

Mathematics Subject Classification ID

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) Global differential geometry of Hermitian and Kählerian manifolds (53C55) Kähler manifolds (32Q15) Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Compact complex (n)-folds (32J18) Jacobians, Prym varieties (14H40) Global theory of symplectic and contact manifolds (53D35) Topological aspects of complex manifolds (32Q55)

Related Items (75)

On the existence of a crepant resolution of some moduli spaces of sheaves on an abelian surface ⋮ The LLV decomposition of hyper-Kähler cohomology (the known cases and the general conjectural behavior) ⋮ Galois representations on the cohomology of hyper-Kähler varieties ⋮ Birational geometry of singular moduli spaces of O'Grady type ⋮ Positivity of Riemann–Roch polynomials and Todd classes of hyperkähler manifolds ⋮ INTERSECTION COHOMOLOGY OF THE MODULI SPACE OF HIGGS BUNDLES ON A GENUS 2 CURVE ⋮ Compact hyper-Kähler categories ⋮ Absolutely trianalytic tori in the generalized Kummer variety ⋮ An inequality for Betti numbers of hyper-Kähler manifolds of dimension 6 ⋮ The Hodge diamond of O’Grady’s six-dimensional example ⋮ Nonsymplectic automorphisms of prime order on O'Grady's sixfolds ⋮ The 2-factoriality of the O'Grady moduli spaces ⋮ Moving and ample cones of holomorphic symplectic fourfolds ⋮ A global Torelli theorem for singular symplectic varieties ⋮ Remarks on projective normality for certain Calabi-Yau and hyperkähler varieties ⋮ Topological invariants of O'Grady's six dimensional irreducible symplectic variety ⋮ Convergence of mean curvature flow in hyper-Kähler manifolds ⋮ Induced automorphisms on irreducible symplectic manifolds: ⋮ Mapping class group and a global Torelli theorem for hyperkähler manifolds ⋮ Base divisors of big and nef line bundles on irreducible symplectic varieties ⋮ Hessian of the natural Hermitian form on twistor spaces ⋮ Geometric description of \(\langle 2\rangle \)-polarised Hilbert squares of generic \(K3\) surfaces ⋮ Groups of symplectic involutions on symplectic varieties of Kummer type and their fixed loci ⋮ The stringy E-function of the moduli space of Higgs bundles with trivial determinant ⋮ The second integral cohomology of moduli spaces of sheaves on K3 and abelian surfaces ⋮ Induced birational transformations on O'Grady's sixfolds ⋮ Rational curves on primitive symplectic varieties of \(\mathrm{OG}_6^s\)-type ⋮ Remarks on Kawamata's effective non-vanishing conjecture for manifolds with trivial first Chern classes ⋮ Symplectic birational transformations of finite order on O'Grady's sixfolds ⋮ Sixfolds of generalized Kummer type and K3 surfaces ⋮ Moduli spaces of stably irreducible sheaves on Kodaira surfaces ⋮ Moduli of double EPW-sextics ⋮ Birational geometry of O'Grady's six dimensional example over the Donaldson-Uhlenbeck compactification ⋮ Unnamed Item ⋮ Symplectic resolutions for Higgs moduli spaces ⋮ The essential skeleton of a product of degenerations ⋮ NEW SYMPLECTIC V-MANIFOLDS OF DIMENSION FOUR VIA THE RELATIVE COMPACTIFIED PRYMIAN ⋮ On the André motive of certain irreducible symplectic varieties ⋮ Monodromy and birational geometry of O'Grady's sixfolds ⋮ On the variety of triangles for a hyper-Kähler fourfold constructed by Debarre and Voisin ⋮ Examples of Irreducible Symplectic Varieties ⋮ Moduli spaces of polarized irreducible symplectic manifolds are not necessarily connected ⋮ On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four ⋮ Moduli spaces of irreducible symplectic manifolds ⋮ SNC Log Symplectic Structures on Fano Products ⋮ The Kodaira dimension and singularities of moduli of stable sheaves on some elliptic surfaces ⋮ On the Beauville form of the known irreducible symplectic varieties ⋮ On monodromies of a degeneration of irreducible symplectic Kähler manifolds ⋮ Singularities of moduli spaces of sheaves on $K3$ surfaces and Nakajima quiver varieties ⋮ The Hodge numbers of O'Grady 10 via Ngô strings ⋮ Lagrangian fibrations on symplectic fourfolds ⋮ Beauville-Bogomolov lattice for a singular symplectic variety of dimension 4 ⋮ Tautological classes on moduli spaces of hyper-Kähler manifolds ⋮ Connected components of moduli spaces of irreducible holomorphic symplectic manifolds of Kummer type ⋮ Singular symplectic moduli spaces ⋮ On the Rozansky-Witten weight systems ⋮ Hasse-Witt invariants of the reductions of certain irreducible symplectic varieties ⋮ Hyper-Kähler compactification of the intermediate Jacobian fibration of a cubic fourfold: The twisted case ⋮ Duality for relative Prymians associated to \(K3\) double covers of del Pezzo surfaces of degree 2 ⋮ The generalized Franchetta conjecture for some hyper-Kähler varieties. II ⋮ Symplectic resolutions of quiver varieties ⋮ On the existence of universal families of marked irreducible holomorphic symplectic manifolds ⋮ The indeterminacy locus of the Voisin map ⋮ Formality conjecture for minimal surfaces of Kodaira dimension 0 ⋮ Unobstructed symplectic packing for tori and hyper-Kähler manifolds ⋮ Holomorphic symplectic geometry: a problem list ⋮ A survey of Torelli and monodromy results for holomorphic-symplectic varieties ⋮ Smoothing of multiple structures on embedded Enriques manifolds ⋮ Enriques manifolds ⋮ On the \(P = W\) conjecture for \(\mathrm{SL}_n\) ⋮ A bound on the second Betti number of hyperkähler manifolds of complex dimension six ⋮ On the motive of O’Grady’s ten-dimensional hyper-Kähler varieties ⋮ La singularité de O’Grady ⋮ Hyper-Kähler manifolds ⋮ A Fourier-Mukai approach to the enumerative geometry of principally polarized abelian surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algebraic geometric interpretation of Donaldson's polynomial invariants
• Variétés kähleriennes dont la première classe de Chern est nulle
• Symplectic structure of the moduli space of sheaves on an abelian or K 3 surface
• On the moduli of vector bundles on an algebraic surface
• Comparison of the Donaldson polynomial invariants with their algebro- geometric analogues
• The first two Betti numbers of the moduli spaces of vector bundles on surfaces
• Duality between D(X) and with its application to picard sheaves
• Desingularized moduli spaces of sheaves on a K3
• The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface
• Moduli of vector-bundles on surfaces
• Some examples of Mukai's reflections on K3 surfaces
• HODGE NUMBERS OF MODULI SPACES OF STABLE BUNDLES ON K3 SURFACES
• Relations among Donaldson polynomials of certain algebraic surfaces, I
• Moduli spaces of stable sheaves on abelian surfaces.

This page was built for publication: A new six-dimensional irreducible symplectic variety