Simone Marchesi, Alex Massarenti, Saeed Tafazolian
Published 2011-05-30, updated 2011-06-02Version 2
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 celebrated results by Ein and Zak.
Comments: 13 pages, corrected reference
Journal: Le Matematiche Vol. LXVI (2011) - Fasc. II, pp. 137-151
Varieties Connected by Chains of Lines
Geometry and Algebra of prime Fano 3-folds of genus 12
Cones of divisors on $\mathbb{P}^3$ blown up at eight very general points
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