Gallego Rodrigo, Francisco JavierGonzalez, M.Purnaprajna, B.P.2023-06-182023-06-1820160021869310.1016/j.jalgebra.2016.06.015https://hdl.handle.net/20.500.14352/24624In this paper, we show that if X is a smooth variety of general type of dimension m≥3 for which the canonical map induces a triple cover onto Y, where Y is a projective bundle over P1 or onto a projective space or onto a quadric hypersurface, embedded by a complete linear series (except Q3 embedded in P4), then the general deformation of the canonical morphism of X is again canonical and induces a triple cover. The extremal case when Y is embedded as a variety of minimal degree is of interest, due to its appearance in numerous situations. For instance, by looking at threefolds Y of minimal degree we find components of the moduli of threefolds X of general type with KX3=3pg−9,KX3≠6, whose general members correspond to canonical triple covers. Our results are especially interesting as well because they have no lower dimensional analogues.engjournal articlehttp://bit.ly/2daOc9Arestricted access512.7Algebraic geometryProjective varieties of general typeGeometria algebraica1201.01 Geometría Algebraica