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

De Poi, Pietro; Mezzetti, Emilia; Sierra, José Carlos

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

Authors

De Poi, Pietro

Mezzetti, Emilia

Sierra, José Carlos

Description

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.
To appear in Advances in Geometry