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

Abstract

For every integer $a\ge 2$, 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.

v2: a new author has been added, results have been strengthened. v3: final version to appear in Bull. London Math. Soc

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