J. Stix proved that a curve of positive genus over $\mathbb{Q}$ which maps to non-trivial Brauer-Severi variety satisfies the section conjecture. We prove that, if $X$ is number field $k$ and Weil restriction $R_{k/\mathbb{Q}}X$ admits rational map variety, then As consequence, $P$ such corestriction $\operatorname{cor}_{k/\mathbb{Q}}([P])\in\operatorname{Br}(\mathbb{Q})$ non-trivial,

The number of apparent double points of a smooth, irreducible projective variety X of dimension n in P is the number of secant lines to X passing through the general point of P. This classical notion dates back to Severi. In the present paper we classify smooth varieties of dimension at most three having one apparent double point. The techniques developed for this purpose allow to treat a wider...

We prove the so-called Unitary Hyperbolicity Theorem, a result on hyperbolicity of unitary involutions. The analogous previously known results for the orthogonal and symplectic involutions are formal consequences of the unitary one. While the original proofs in the orthogonal and symplectic cases were based on the incompressibility of generalized Severi-Brauer varieties, the proof in the unitar...

Based on results by Brugallé and Mikhalkin, Fomin and Mikhalkin give formulas for computing classical Severi degreesN using long-edge graphs. In 2012, Block, Colley and Kennedy considered the logarithmic version of a special function associated to long-edge graphs which appeared in Fomin-Mikhalkin’s formula, and conjectured it to be linear. They have since proved their conjecture. At the same t...