Singularity formation in co-dimension one of the dHYM cotangent flow on blow up of CP³ at a point

The existence and uniqueness of canonical singular solutions of the J equation and the deformed Hermitian Yang Mills (dHYM) equation was proved in [11] on compact Kähler surfaces. In this paper, we study the singularity formation of the dHYM cotangent flow on the one-point blow up of CP³ using Calabi ansatz. In particular, we provide an explicit example where the flow develops a singularity along the exceptional divisor. Moreover, the limit satisfies corresponding singular dHYM equation in the sense of [11] and provides some evidence for Conjecture $1.12$ in [11] on this three dimensional manifold with symmetry.