On the blow-up formula of the Chow weights for polarized toric manifolds

Let X be a smooth projective toric variety and let X be the blow-up manifold of X at finitely many distinct tours invariants points of X. In this paper, we give an explicit combinatorial formula of the Chow weight of X in terms of the base toric manifold X and the symplectic cuts of the Delzant polytope. We then apply this blow-up formula to the projective plane and see the difference of Chow stability between the toric blow-up manifolds and the manifolds of blow-ups at general points. Finally, we detect the blow-up formula of the Futaki-Ono invariant which is an obstruction for asymptotic Chow semistability of a polarized toric manifold.