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)

Abstract

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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.

Published
2011-12-14
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: <https://lematematiche.dmi.unict.it/index.php/lematematiche/article/view/844>. Date accessed: 26 sep. 2017.
Section
Articoli

Keywords

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