The K-energy on hypersurfaces and stability (Q1903149)

Let \(f\) be a homogeneous polynomial on \(\mathbb{C}^{n + 2}\) of degree \(d\) and \(\Sigma_f\) the corresponding hypersurface in \(\mathbb{C} P^{n + 1}\). Then condititions are given in terms of a generalised \(K\)-energy for \(\Sigma_f\) to be stable or semistable. As an application, if \(\Sigma_f\) is a normal hypersurface, has only log-terminal singularities and \(d \geq n + 2\) then \(\Sigma_f\) is stable.