A characterization of cones in PG(3, q) as sets of points of PG(3, q) of size q2 + q + 1 projecting from a point V a set of q + 1 points of a plane of PG(3, q) and with three intersection numbers with respect to the planes is given.

On (q2+q+1)-sets of class [1,m,n]2 in PG(3,q)

On sets of type (m,n )r-1 in PG(r,q)

It is proved that a k–set of type (q + 1, n)2 in PG(3, q) either is a plane or it has size k ≥ (q + 1)2 and a characterization of some sets of size (q + 1)2 is given.

On sets of type ( q + 1, n ) 2 in finite three-dimensional projective spaces

In this paper we prove that, in PG(3, q), q odd, a (q 2 + q +1)-set of type ((n − 1)q + 1, nq + 1, (n + 1)q + 1)2, 1 ≤ n ≤ q, and type (a, b, c, d)1, with , such that any external line is contained in exactly one ((n − 1)q + 1)-secant plane is a parabolic quadric.

A combinatorial characterization of parabolic quadrics

We prove that only one irreducible cubic, either with a node or with a cusp or with an isolated double point, containing the maximum number of points of PG(2, 2) exists.

On some singular irreducible cubics of PG(2, 2)

In this paper we prove that in a projective space of dimension three and orderq the two plane characterk-sets forke {q 2+ 1,(q+1)2} are of the same type as the elliptic or the hyperbolic quadric, respectively. As a corollary we obtain a characterization of the elliptic and the hyperbolic quadrics.

A combinatorial characterization of quadrics

We prove that two irreducible cubics containing the maximum number of points, that is five, of a Fano plane exist and result to be projectively equivalent.

On the irreducible cubics containing the maximum number of points of a Fano plane

We consider the cubic curves of PG(2, 3) and we prove that those containing the maximum number of points of PG(2, 3), irreducible over PG(2, Γ3), are two.

The cubic curves of PG(2, 3)

We consider the singular absolutely irreducible cubics of PG(2, 3) and we prove that one with a node, two with a cusp and one with an isolated double point exist.

Stefania Ferri

Papers

A combinatorial characterization of quadrics

On the irreducible cubics containing the maximum number of points of a Fano plane

On some singular irreducible cubics of PG(2, 2)

The cubic curves of PG(2, 3)

The singular absolutely irreducible cubics of PG(2, 3)