Osaka Journal of Mathematics

Chow-stability and Hilbert-stability in Mumford's geometric invariant theory

Toshiki Mabuchi

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In this note, we shall show that Chow-stability and Hilbert-stability in GIT asymptotically coincide. The proof in [5] is simplified in the present form, while a quick review is in [6].

Article information

Osaka J. Math., Volume 45, Number 3 (2008), 833-846.

First available in Project Euclid: 17 September 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14L24: Geometric invariant theory [See also 13A50] 32Q15: Kähler manifolds
Secondary: 32Q20: Kähler-Einstein manifolds [See also 53Cxx] 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)


Mabuchi, Toshiki. Chow-stability and Hilbert-stability in Mumford's geometric invariant theory. Osaka J. Math. 45 (2008), no. 3, 833--846.

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