Abstract We prove the Zariski dense orbit conjecture in positive characteristic for regular self-maps of split semiabelian varieties.

let $r$ be an associative ring and let $m$ be a left $r$-module.let $spec_{r}(m)$ be the collection of all prime submodules of $m$ (equipped with classical zariski topology). there is a conjecture which says that every irreducible closed subset of $spec_{r}(m)$ has a generic point. in this article we give an affirmative answer to this conjecture and show that if $m$ has a noetherian spectrum, t...

after the classification of the flag-transitive linear spaces, the attention has been turned to line-transitive linear spaces. in this article, we present a partial classification of the finite linear spaces $mathcal s$ on which an almost simple group $g$ with the socle $g_2(q)$ acts line-transitively.

We define a topological invariant of complex projective plane curves. As an application, we present new examples of arithmetic Zariski pairs.

The main result implies that a proper convex subset of an irreducible higher rank symmetric space cannot have Zariski dense stabilizer.