A well-known conjecture asserts that smooth threefolds X in 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 in P^5 is not quadratically normal, then its triple curve is reducible. Similar results are also given for higher dimensional varieties.
On the quadratic normality and the triple curve of three dimensional subvarieties of P^5 / De Poi, P.; Mezzetti, Emilia; Sierra, J. C.. - In: ADVANCES IN GEOMETRY. - ISSN 1615-715X. - STAMPA. - Advances in Geometry. Volume 10, Issue 3, 2010:(2010), pp. 419-426. [10.1515/ADVGEOM.2009.038]
On the quadratic normality and the triple curve of three dimensional subvarieties of P^5
MEZZETTI, EMILIA;
2010-01-01
Abstract
A well-known conjecture asserts that smooth threefolds X in 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 in P^5 is not quadratically normal, then its triple curve is reducible. Similar results are also given for higher dimensional varieties.Pubblicazioni consigliate
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