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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 14, Issue 4


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

Kota Hattori
Published Online: 2014-10-08 | DOI: https://doi.org/10.1515/advgeom-2014-0009


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.

About the article

Published Online: 2014-10-08

Published in Print: 2014-10-01

Citation Information: Advances in Geometry, Volume 14, Issue 4, Pages 613–630, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2014-0009.

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