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• W3211095450 abstract "Consider a compact Kahler manifold which either admits an extremal Kahler metric, or is a small deformation of such a manifold. We show that the blowup of the manifold at a point admits an extremal Kahler metric in Kahler classes making the exceptional divisor sufficiently small if and only if it is relatively K-stable, thus proving a special case of the Yau-Tian-Donaldson conjecture. We also give a geometric interpretation of what relative K-stability means in this case in terms of finite dimensional geometric invariant theory. This gives a complete solution to a problem addressed in special cases by Arezzo, Pacard, Singer and Sz'ekelyhidi. In addition, the case of a deformation of an extremal manifold proves the first non-trivial case of a general conjecture of Donaldson." @default.
• W3211095450 created "2021-11-08" @default.
• W3211095450 creator A5020993951 @default.
• W3211095450 creator A5070389295 @default.
• W3211095450 date "2021-10-26" @default.
• W3211095450 modified "2023-09-27" @default.
• W3211095450 title "Extremal Kahler metrics on blowups" @default.
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• W3211095450 hasPublicationYear "2021" @default.
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