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

研究成果: Article査読

2 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)613-630
ページ数18
ジャーナルAdvances in Geometry
14
4
DOI
出版ステータスPublished - 2014 10 1
外部発表はい

ASJC Scopus subject areas

  • Geometry and Topology

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