TY - JOUR
T1 - Asymptotic stability for Kähler–Ricci solitons
AU - Takahashi, Ryosuke
N1 - Funding Information:
The author would like to express his gratitude to Professor Ryoichi Kobayashi for his advice on this article, and to the referee for useful suggestions that helped him to improve the original manuscript. The author is supported by Grant-in-Aid for JSPS Fellows Number 25-3077.
Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.
PY - 2015/12/1
Y1 - 2015/12/1
N2 - 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}.
AB - 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}.
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U2 - 10.1007/s00209-015-1518-4
DO - 10.1007/s00209-015-1518-4
M3 - Article
AN - SCOPUS:84947045350
VL - 281
SP - 1021
EP - 1034
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 3-4
ER -