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

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

2008-11-10

arxiv.org/abs/0811.1515v1

Mathematics

Algebraic Geometry

To appear in Advances in Geometry

Scientific paper

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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