TY - JOUR
T1 - The holomorphic symplectic structures on hyper-Kähler manifolds of type A∞
AU - Hattori, Kota
N1 - Publisher Copyright:
© 2014 by Walter de Gruyter Berlin/Boston.
PY - 2014/10/1
Y1 - 2014/10/1
N2 - 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 C×-actions on these manifolds, and we give sufficient and necessary conditions for the existence of C×-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.
AB - 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 C×-actions on these manifolds, and we give sufficient and necessary conditions for the existence of C×-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.
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U2 - 10.1515/advgeom-2014-0009
DO - 10.1515/advgeom-2014-0009
M3 - Article
AN - SCOPUS:84908082712
SN - 1615-715X
VL - 14
SP - 613
EP - 630
JO - Advances in Geometry
JF - Advances in Geometry
IS - 4
ER -