On unexpected curves of type (d+k,d)

We present a construction explaining the existence of (unexpected) curves of degree $d+k$, passing through a set Z of points on P², and having a generic point P of multiplicity d. The construction is based on the syzygies of the k-th powers of Jacobian of the product of lines dual to the points of Z. We prove also a result characterizing the unexpectedness of the curves via splitting type of the bundle of these syzygies retricted to the line dual to P.