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Deformations of canonical triple covers



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Gallego Rodrigo, Francisco Javier and Gonzalez, M. and Purnaprajna, B.P. (2016) Deformations of canonical triple covers. Journal of Algebra, 463 (1). pp. 1-9. ISSN 00218693

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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 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.

Item Type:Article
Uncontrolled Keywords:Algebraic geometry; Projective varieties of general type
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:39250
Deposited On:07 Oct 2016 12:04
Last Modified:10 Oct 2016 08:52

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