We show that the underlying complex manifold of a complete noncompact twodimensional shrinking gradient KählerRicci soliton (M,g,X) with soliton metric g with bounded scalar curvature Rg whose soliton vector field X has an integral curve along which Rg↛0 is biholomorphic to either C×P1 or to the blowup of this manifold at one point. Assuming the existence of such a soliton on this latter manifold, we show that it is toric and unique. We also identify the corresponding soliton vector field. Given these possibilities, we then prove a strong form of the FeldmanIlmanenKnopf conjecture for finite time Type I singularities of the KählerRicci flow on compact Kähler surfaces, leading to a classification of the bubbles of such singularities in this dimension.
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Steady gradient KählerRicci solitons on crepant resolutions of CalabiYau cones
We show that, up to the flow of the soliton vector field, there exists a unique complete steady gradient KählerRicci soliton in every Kähler class of an equivariant crepant resolution of a CalabiYau cone converging at a polynomial rate to Cao's steady gradient KählerRicci soliton on the cone.
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 Award ID(s):
 2109577
 NSFPAR ID:
 10332208
 Date Published:
 Journal Name:
 ArXivorg
 ISSN:
 23318422
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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