We give a bound for the number of rational maps between algebraic varietiesof general type under mild hypothesis on the canonical map. We use an ideainspired by Tanabe's work. Instead of attaching a morphism of Hodge structuresto a rational map we simply associate to it a piece of the integral Hodgelattice. This procedure does not give an injective map, but by means of ageometric argument, we can estimate the number of maps with the same image.
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