Deformations of canonical triple covers

作者：Javier Gallego Francisco; Gonzalez Miguel^*; Purnaprajna Bangere P

来源：Journal of Algebra, 2016, 463: 1-9.

DOI：10.1016/j.jalgebra.2016.06.015

• Algebraic geometry
• Projective varieties of general type

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 PI or onto a projective space or onto a quadric hypersurface, embedded by a complete linear series (except Q(3) embedded in P-4), 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 K-X(3) = 3p(g) - 9, K-X(3) not equal 6, whose general members correspond to canonical triple covers. Our results are especially interesting as well because they have no lower dimensional analogues.

• 出版日期2016-10-1