pluricanonical

— Our main result is that, on the projective completion #92;mathbb#123;P#125;(#92;mathcal#123;F#125;#92;oplus#92;mathbb#123;C#125;) of a pluricanonical line bundle #92;mathcal#123;F#125;} over a product of K\"ahler--Einstein Fano manifolds with the second Betti number 1, momentum-constructed constant scalar curvature K\"ahler metrics with cone singularities along the #92;infty-section exist if and only if the log Futaki invariant vanishes on the fibrewise #92;mathbb#123;C#125;#42;-action, giving a supporting evidence to the log version of the Donaldson--Tian--Yau conjecture for general polarisations.