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)
Keywords: Conic-connected varieties, covered by lines, dual and secant defective, Hartshorne Conjecture


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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.