| It is well-known that the derived category of coherent sheaves on a projective line is equivalent to the derived category of representations of the Kronecker quiver. In my talk (based on a joint work with Yuriy Drozd) I am going to show that the perfect derived category of coherent sheaves of an arbitrary reduced rational projective curve can be fully faithfully embedded into the derived category of representations of an appropriate finite dimensional algebra of finite global dimension. In the case of degenerate elliptic curves of type of Kodaira type $I_n$ (cycles of projective lines), this construction leads to a particularly beautiful class of algebras, called gentle. As an application of the developed theory, I am going to show that the Rouquier dimension of the derived category of coherent sheaves on a cycle of projective lines is equal to one. |