Maximum number of points on an intersection of a cubic threefold and a non-degenerate Hermitian threefold

In algebraic geometry, it is important to provide effective parametrizations for families of curves, both in theory and in practice. In this paper, we present such an effective parametrization for the moduli of genus-5 curves that are neither ...

Segre (Ann Mat Pura Appl 48:1---96, 1959 ) mentioned that the number $$N$$ N of points on a curve which splits into $$k$$ k distinct lines on the projective plane over a finite field of order $$q$$ q satisfies $$kq - \frac{k(k-3)}{2} \le N \le kq+1.$$ k q - k ( k - 3 ) 2 ≤ N ≤ k q + 1 . We see that the upper bound is satisfactory, but the lower one ...

New infinite families of hyperovals of the generalized quadrangle H(3,q^2) are provided. They arise in different geometric contexts. More precisely, we construct hyperovals by means of certain subsets of the projective plane called here k-tangent arcs ...