Equivariant deformations of meromorphic actions on compact complex manifolds

Nobuhiro Honda

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Meromorphicity is the most basic property for holomorphic ℂ*-actions on compact complex manifolds. We prove that the meromorphicity of ℂ*-actions on compact complex manifolds are not necessarily preserved by small deformations, if the complex dimension of complex manifolds is greater than two. In contrast, we also show that the meromorphicity of ℂ*-actions on compact complex surface depends only on the topology (the first Betti number) of the surface. We construct such examples of dimension greater than two by studying an equivariant deformation of certain complex threefold, so called a twistor space.

Original languageEnglish
Pages (from-to)469-481
Number of pages13
JournalMathematische Annalen
Volume319
Issue number3
DOIs
Publication statusPublished - 2001 Jan 1

ASJC Scopus subject areas

  • Mathematics(all)

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