4 problems

Classification conjecture. The first order congruences whose pure fundamental locus $F$ is a smooth variety of codimension two are precisely those obtained in the classification th…

Let $S$ be a smooth surface embedded in ${\bf P}^{6}$ with no trisecant lines. The authors construct a list of such surfaces, including cases with and without lines, and distinguis…

Let $\mathcal{C}\subset\operatorname{\mathbb{P}}^r$, let $\mathbb{L}$ be its unique trisecant line, and set … Assume these objects are as in the paper's second main theorem. The ra…

Let $\mathrm{PG}(2,q)$ be a projective plane of odd order $q$, and let a $(q+2)$-set be a point set with $q+2$ points. An odd-secant is a line meeting the set in an odd number of p…