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.

We investigate the Zariski Topology on the L-prime spectrum of modules consisting of the collection of all prime Lsubmodules and prove some useful results.

We give examples of non-isotrivial K3 surfaces over complex function fields with Zariski-dense rational points and NéronSeveri rank one.