Abstract
Assume that a projective variety together with a polarization is uniformly K-stable. If the polarization is canonical or anti-canonical, then the projective variety is uniformly K-stable with respects to any polarization sufficiently close to the original polarization.
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Acknowledgements
This work started while the author enjoyed the AIM workshop “Stability and Moduli Spaces”. The author thanks the organizers and staff for the stimulating environment. During and after the workshop, the author learned many motivations and backgrounds from Doctors Giulio Codogni and Ruadhaí Dervan. Especially, they helped the author to improve Theorem 3 (see also Remark 6). The author thanks the referee for helpful comments. The author is supported by JSPS KAKENHI Grant Number JP16H06885.
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Communicated by Ngaiming Mok.
