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

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.

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