In one sense, deformation theory is as old as algebraic geometry itself: this is because all
algebro-geometric objects can be “deformed” by suitably varying the coef? cients of their …

The number of apparent double points of a smooth, irreducible projective variety $ X $ of
dimension $ n $ in $\Proj^{2n+ 1} $ is the number of secant lines to $ X $ passing through …

The first part of this note contains a review of basic properties of the variety of lines
contained in an embedded projective variety and passing through a general point. In …

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We introduce and study projective varieties X^ r+ 1 ⊂ P^ N of dimension r+ 1 which are n-
covered by irreducible curves of degree δ≥ n− 1≥ 1, that is, varieties such that through n …

We recall the statements of Hartshorne's Conjecture on Complete Intersections and of
Hartshorne's Conjecture on Linear Normality. In Theorem 5.1. 6 we present Zak's proof of …

We recall the definition of QEL, respectively LQEL, manifolds as those X ⊂ P^ N whose
general entry locus is a quadric hypersurface of dimension equal to the secant defect of X …

We recall without proofs the basic definitions and results, leading to the construction of
various Hilbert Schemes and describing the infinitesimal properties of these parameter …