Asymptotic stability for Kähler–Ricci solitons

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Abstract

Let X be a Fano manifold. We say that a hermitian metric ϕ on -KX with positive curvature ωϕ is a Kähler–Ricci soliton if it satisfies the equation (Formula Presented.) for some holomorphic vector field VKS. The candidate for a vector field VKS is uniquely determined by the holomorphic structure of X up to conjugacy, hence depends only on the holomorphic structure of X. We introduce a sequence {Vk} of holomorphic vector fields which approximates VKS and fits to the quantized settings. Moreover, we also discuss about the existence and convergence of the quantized Kähler–Ricci solitons attached to the sequence {Vk}.

Original languageEnglish
Pages (from-to)1021-1034
Number of pages14
JournalMathematische Zeitschrift
Volume281
Issue number3-4
DOIs
Publication statusPublished - Dec 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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