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Licensed Unlicensed Requires Authentication Published by De Gruyter October 8, 2014

The holomorphic symplectic structures on hyper-Kähler manifolds of type A∞

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From the journal Advances in Geometry


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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