A gluing construction of constant scalar curvature Kähler metrics of Poincaré type

We consider a compact Kähler manifold admitting a constant scalar curvature Kähler metric and with no nontrivial holomorphic vector fields. After blowing up the manifold at finitely many points, we prove the existence of constant scalar curvature Kähler metrics on the complement of the exceptional divisors, with Poincaré-type singularities along them.