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In this note we clarify the structure of the moduli space of constant scalarcurvature Kaehler metrics as one approaches the boundary of the Kaehler cone oncscK manifolds blown up at finite set of points, in the spirit of the previouswork arXiv:math/0504115. Results about which Kaehler classes can be reached andabout the position of the blown up points are given.

On the K\"ahler classes of constant scalar curvature metrics on blow ups