On the quadratic normality and the triple curve of three dimensional subvarieties of ${\mathbb P}^5$

Pietro De Poi; Emilia Mezzetti; José Carlos Sierra

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arXiv · 0811.1515

On the quadratic normality and the triple curve of three dimensional subvarieties of ${\mathbb P}^5$

Pietro De Poi·Emilia Mezzetti·José Carlos Sierra

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Abstract

A well-known conjecture asserts that smooth threefolds $X\subset\{\mathbb P}^5$ are quadratically normal with the only exception of the Palatini scroll. As a corollary of a more general statement we obtain the following result, which is related to the previous conjecture: If $X\subset\{\mathbb P}^5$ is not quadratically normal, then its triple curve is reducible. Similar results are also given for higher dimensional varieties.

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Pietro De Poi, Emilia Mezzetti, José Carlos Sierra. 2008-11-10. On the quadratic normality and the triple curve of three dimensional subvarieties of ${\mathbb P}^5$. https://arxiv.org/abs/0811.1515

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