%0 Journal Article
%T Covered by lines and Conic connected varieties Covered by lines and Conic connected varieties
%A Alex Massarenti
%A Simone Marchesi
%A Saeed Tafazolian
%J Le Matematiche
%D 2011
%I University of Catania
%X We study some properties of an embedded variety covered by lines and give a numerical criterion ensuring the existence of a singular conic through two of its general points. We show that our criterion is sharp. Conic-connected, covered by lines, QEL, LQEL, prime Fano, defective, and dual defective varieties are closely related. We study some relations between the above mentioned classes of objects using basic results by Ein and Zak. p, li { white-space: pre-wrap; } We study some properties of an embedded variety covered by lines and give a numerical criterion ensuring the existence of a singular conic through two of its general points. We show that our criterion is sharp. Conic-connected, covered by lines, $QEL$, $LQEL$, prime Fano, defective, and dual defective varieties are closely related. We study some relations between the above mentioned classes of objects using basic results by Ein and Zak.
%K Conic-connected varieties
%K covered by lines
%K dual and secant defective
%K Hartshorne Conjecture
%U http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/844