Corrado Zanella

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The aim of this paper is to present a construction of t-divisible designs for t > 3, because such divisible designs seem to be missing in the literature. To this end, tools such as finite projective spaces and their algebraic varieties are employed. More precisely, in a first step an abstract construction, called t-lifting, is developed. It starts from a(More)
Let S(Π0,Π1) be the product of the projective spaces Π0 and Π1, i.e. the semilinear space whose point set is the product of the point sets of Π0 and Π1, and whose lines are all products of the kind {P0}×g1 or g0×{P1}, where P0, P1 are points and g0, g1 are lines. An embedding χ : S(Π0,Π1) → Π′ is an injective mapping which maps the lines of S(Π0,Π1) onto(More)
In this paper both blocking sets with respect to the s-subspaces and covers with t-subspaces in a finite Grassmannian are investigated, especially focusing on geometric descriptions of blocking sets and covers of minimum size. When such a description exists, it is called a Bose–Burton type theorem. The canonical example of a blocking set with respect to the(More)
The quadratic Veronese embedding ρ maps the point set P of PG(n, F ) into the point set of PG( (n+2 2 ) − 1, F ) (F a commutative field) and has the following well-known property: If M ⊂ P, then the intersection of all quadrics containing M is the inverse image of the linear closure of Mρ. In other words, ρ transforms the closure from quadratic into linear.(More)
A linear partial spread is a set of mutually skew lines of some P(V ) – where V is a finite dimensional vector space over a field – that are characterized by the property that their images under the Plücker embedding are in a given subspace of P (∧2 V ); it is a linear spread if the lines in it cover the whole space. We will provide methods to construct(More)