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arXiv · 1511.06922

Deformations of canonical triple covers

Francisco Javier Gallego·Miguel Gonzalez·Bangere P. Purnaprajna
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Abstract

In this paper, we show that if $X$ is a smooth variety of general type of dimension $m \geq 3$ for which the canonical map induces a triple cover onto $Y$, where $Y$ is a projective bundle over $\mathbf P^1$ 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.

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Francisco Javier Gallego, Miguel Gonzalez, Bangere P. Purnaprajna. 2015-11-21. Deformations of canonical triple covers. https://arxiv.org/abs/1511.06922

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