Nets of conics over finite fields

A conic in a projective plane is the zero locus of a quadratic form in F[X, Y, Z]. Linear systems of conics are subspaces of the vector space of quadratic forms in F[X, Y, Z], and they are called nets when of projective dimension two. Nets of conics (over the reals and the complex numbers) were already studied by Camille Jordan in 1906, although a complete classification for these fields was only given by Charles T. C. Wall in 1977. For finite fields, Albert Wilson, in 1914, studied the odd characteristic case, and Alan D. Campbell studied the even characteristic case in 1928, but none of these treatments contains a complete classification. Conics correspond to hyperplanes (or hyperplane sections) of the Veronesean quadric in P^5 and nets of conics correspond to planes (subspaces of co-dimension 3) in P^5. In this talk we will explain these connections and then focus on recent results concerning the classification of nets of conics over finite fields.

We are looking forward to meeting you at FAMNIT-VP1. 

This Thursday, September 8,  2022, from 14:00 to 15:00.

 Everyone is welcome and encouraged to attend.