2015/11/21 by Gallego, Francisco Javier, Gonzalez, Miguel, Purnaprajna, Bangere P.
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1511.06922
In 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 \mathbf P1 or onto a projective space or onto a quadric hypersurface, embedded by a complete linear series, 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. This is especially interesting as well, since it has no lower dimensional analogues.