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The holomorphic symplectic structures on hyper-Kähler manifolds of type A∞
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Kota Hattori
Published/Copyright:
October 8, 2014
Abstract
Hyper-Kähler manifolds of type A∞ are noncompact complete Ricci-flat Kähler manifolds of complex dimension 2. We study the holomorphic symplectic structures preserved by the natural ℂx-actions on these manifolds, and we give sufficient and necessary conditions for the existence of ℂx-equivariant biholomorphisms between two hyper-Kähler manifolds of type A∞ preserving their holomorphic symplectic structures. As a consequence, we can show the existence of a complex manifold of dimension 2 on which there is a continuous family of complete Ricci-flat Kähler metrics with distinct volume growth.
Published Online: 2014-10-8
Published in Print: 2014-10-1
© 2014 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- On the type number of a hypersurface in the 6-dimensional sphere
- On the equality case in Ehrhart’s volume conjecture
- Hamiltonian stability of Hamiltonian minimal Lagrangian submanifolds in pseudo- and para-Kähler manifolds
- The holomorphic symplectic structures on hyper-Kähler manifolds of type A∞
- Bifurcation values and stability of algebras of bounded polynomials
- Families of bitangent planes of space curves and minimal non-fibration families
- On deformations of G2-structures by Killing vector fields
- Cohomology of 3-points configuration spaces of complex projective spaces
- Slope stability of Fano fourfolds with respect to smooth surfaces
- On quartics with lines of the second kind
Articles in the same Issue
- Frontmatter
- On the type number of a hypersurface in the 6-dimensional sphere
- On the equality case in Ehrhart’s volume conjecture
- Hamiltonian stability of Hamiltonian minimal Lagrangian submanifolds in pseudo- and para-Kähler manifolds
- The holomorphic symplectic structures on hyper-Kähler manifolds of type A∞
- Bifurcation values and stability of algebras of bounded polynomials
- Families of bitangent planes of space curves and minimal non-fibration families
- On deformations of G2-structures by Killing vector fields
- Cohomology of 3-points configuration spaces of complex projective spaces
- Slope stability of Fano fourfolds with respect to smooth surfaces
- On quartics with lines of the second kind
