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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173789A 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 GeometryAlgebraic Geometry14M07; 14N05On the quadratic normality and the triple curve of three dimensional subvarieties of ${\mathbb P}^5$text