Covered by lines and Conic connected varieties

  • Alex Massarenti SISSA
  • Simone Marchesi Universit√† degli studi di Milano - Universidad Complutense de Madrid
  • Saeed Tafazolian School of Mathematics, Institute for Research in Fundamental Sciences (IPM) - Institute for Advanced Studies in Basic Sciences (IASBS)


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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.

How to Cite
MASSARENTI, Alex; MARCHESI, Simone; TAFAZOLIAN, Saeed. Covered by lines and Conic connected varieties. Le Matematiche, [S.l.], v. 66, n. 2, p. 137-151, dec. 2011. ISSN 2037-5298. Available at: <>. Date accessed: 26 sep. 2017.


Conic-connected varieties; covered by lines; dual and secant defective; Hartshorne Conjecture