Abstract
Q is a quiver of type if its graph is of affine type and if its arrows have a certain orientation. We develop a bijection between the set of indecomposable kQ-modules whose dimension vectors are positive real roots of the root system associated to Q and a certain set of planar curves. We prove that the number of self-intersections of the curve which corresponds to the module M is equal to the dimension of . We also prove that, for many pairs of modules (M, N), the number of intersections between the corresponding two curves is equal to the dimension of , where C is the cluster category of kQ-mod.
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