On the quadratic normality and the triple curve of three dimensional subvarieties of \mathbb P⁵

2008/11/10 by Pietro De Poi, De Poi, Pietro, Emilia Mezzetti +3
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.0811.1515

Abstract

A well-known conjecture asserts that smooth threefolds X⊂\\mathbb P⁵ 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⊂\\mathbb P⁵ is not quadratically normal, then its triple curve is reducible. Similar results are also given for higher dimensional varieties.

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