On K-stability of some del Pezzo surfaces of Fano index 2

Published 10 Nov 2020 in math.AG and math.DG | (2011.05094v3)

Abstract: For every integer $a \geq 2$, we relate the K-stability of hypersurfaces in the weighted projective space $\mathbb{P}(1,1,a,a)$ of degree $2a$ with the GIT stability of binary forms of degree $2a$. Moreover, we prove that such a hypersurface is K-polystable and not K-stable if it is quasi-smooth.

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