We investigate certain alternating matrices of linear forms whose Pfaffians generate the homogeneous ideal of an elliptic normal curve, or one of its higher secant varieties.

Secant varieties to Veronese embeddings of projective space are classical varieties whose equations are not completely understood. Minors of catalecticant matrices furnish some of their equations, and in some situations even generate their ideals. Geramita conjectured that this is the case for the secant line variety of the Veronese variety, namely that its ideal is generated by the 3×3 minors ...

We classify, under reasonable assumptions, all differentiable functions f for which the ‘secant method’ [xf(y) − yf(x)]/[f(y) − f(x)] is continuous and associative. Further, we classify all differentiable functions for which the similar type of addition xf(y) + yf(x) is associative.

We study the point-line incidence structures of nonsingular points and hyperbolic secant lines associated with ovoids in finite orthogonal spaces. We show that these incidence structures frequently produce partial linear spaces and the parameters of the bipartite graphs (called ovoidal graphs) associated with these structures produce simple and effective isomorphism invariants to distinguish no...

Let U be the classical unital in PG(2, q2) secant to `∞. By deriving PG(2, q) with respect to a derivation set disjoint from U we obtain a new unital U ′ in the Hall plane of order q2. We show that this unital contains O’Nan configurations and is not isomorphic to the known unitals of the Hall plane, hence it forms a new class of unitals in the Hall plane.

Let Xm,n be the Segre-Veronese variety Pm×Pn embedded by the morphism given by O(1, 2) and let σs(Xm,n) denote the sth secant variety to Xm,n. In this paper, we prove that if m = n or m = n+1, then σs(Xm,n) has the expected dimension except for σ6(X4,3). As an immediate consequence, we will give function s1(m,n) ≤ s2(m,n) such that if s ≤ s1(m,n) or if s ≥ s2(m,n), then σs(Xm,n) has the expecte...

In this paper we prove that in PG(3, q) a q 4+q2 2 −set of lines, having exactly q8−q7−q4+q3 8 pairs of skew lines, of type (m,m+ q 2+q 2 ) with respect to stars of lines and of type (m′,m′ + q 2+q 2 ) with respect to ruled planes, is the set of lines either external to or secant to an ovoid.

Consider a polar space S weakly embedded in a projective space P. A secant of S is the intersection of the point set of S with a line of P spanned by two non-collinear points of S. The geometry consisting of the points of S and as lines the secants is a so-called Delta space. In this paper we give a characterization of this and some related geometries.