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Deformations of canonical double covers

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Gallego Rodrigo, Francisco Javier and Gonzalez, M. and Purnaprajna, B.P. (2016) Deformations of canonical double covers. Journal of Algebra, 463 (1). pp. 23-32. ISSN 00218693

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Abstract

In this paper we show that if X is a smooth variety of general type of dimension m≥2 for which its canonical map induces a double cover onto Y, where Y is the projective space, a smooth quadric hypersurface or a smooth projective bundle over P1, embedded by a complete linear series, then the general deformation of the canonical morphism of X is again canonical and induces a double cover. The second part of the article proves the non-existence of canonical double structures on the rational varieties above mentioned. Our results have consequences for the moduli of varieties of general type of arbitrary dimension, since they show that infinitely many moduli spaces of higher dimensional varieties of general type have an entire “hyperelliptic” component. This is in sharp contrast with the case of curves or surfaces of lower Kodaira dimension.


Item Type:Article
Uncontrolled Keywords:Algebraic geometry; Projective varieties of general type
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:39253
Deposited On:07 Oct 2016 12:04
Last Modified:10 Oct 2016 08:50

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