Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 71, Number 3 (2019), 861-880.
Relative stability associated to quantised extremal Kähler metrics
We study algebro-geometric consequences of the quantised extremal Kähler metrics, introduced in the previous work of the author. We prove that the existence of quantised extremal metrics implies weak relative Chow polystability. As a consequence, we obtain asymptotic weak relative Chow polystability and relative $K$-semistability of extremal manifolds by using quantised extremal metrics; this gives an alternative proof of the results of Mabuchi and Stoppa–Székelyhidi. In proving them, we further provide an explicit local density formula for the equivariant Riemann–Roch theorem.
J. Math. Soc. Japan, Volume 71, Number 3 (2019), 861-880.
Received: 23 February 2018
First available in Project Euclid: 25 April 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 32Q26: Notions of stability
Secondary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]
HASHIMOTO, Yoshinori. Relative stability associated to quantised extremal Kähler metrics. J. Math. Soc. Japan 71 (2019), no. 3, 861--880. doi:10.2969/jmsj/79947994. https://projecteuclid.org/euclid.jmsj/1556179398