题目：Deformation theory of scalar flat kahler ALE metrics

报告人：jiyuan Han，University  of Wisconsin-Madison.

时间：7月18日 周一 下午2:00-4:00

地点：管研楼1218

摘要: We prove a Kuranishi-type theorem for deformations of complex structures on ALE K/"ahler surfaces. This is used to prove that for any scalar-flat K/"ahler ALE surface, all small deformations of complex structure also admit scalar-flat K/"ahler ALE metrics. A local moduli space of scalar-flat K/"ahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat K/"ahler ALE surface which deforms to a minimal resolution of C2/Γ, where Γ is a finite subgroup of U(2) without complex reflections.

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