In dimension 1 and 2 and over an algebraically closed field of characteristic 0, unirationality implies rationality (hence a fortiori stable rationality). In the surface case, this follows from the Castenuovo characterization of smooth projective rational surfaces as those smooth projective surfaces X satisfying q(X) = p2(X) = 0 (see [5]). Starting from dimension 3, the answer to the Lüroth pro...

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

In this short note, we show that K-semistable Fano manifolds with the smallest alpha invariant are projective spaces. Singular cases are also investigated.

On this note we prove that a holomorphic foliation of the projective plane with rich, but finite, automorphism group does not have invariant algebraic curves.

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

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

We present a simple rational map of the complex projective plane whose first and second dynamical degrees coincide, but which does not have any invariant foliation.

We show that the fundamental group is not invariant under derived equivalence of smooth projective varieties. 2010 Mathematics Subject Classification. Primary 14-F05; Secondary 14-F35.