Related papers: A smooth complex rational affine surface with unco…

We construct a smooth complex projective rational surface with infinitely many mutually non-isomorphic real forms. This gives the first definite answer to a long standing open question if a smooth complex projective rational surface has…

For any positive integer $r$, we construct a smooth complex projective rational surface which has at least $r$ real forms not isomorphic over $\mathbb{R}$.

We prove that any smooth rational projective surface over the field of complex numbers has an open covering consisting of 3 subsets isomorphic to affine planes.

We classify smooth surfaces whose higher cohomologies of i-forms for all i vanish. We show that if such a surface is not affine, then it has essentially two possibilities.

The aim of this paper is twofold. First of all, we confirm a few basic criteria of the finiteness of real forms of a given smooth complex projective variety, in terms of the Galois cohomology set of the discrete part of the automorphism…

We survey some results on real rational surfaces focused on their topology and their birational geometry.

We describe a family of rational affine surfaces S with huge groups of automorphisms in the following sense: the normal subgroup of Aut(S) generated by all its algebraic subgroups is not generated by any countable family of such subgroups,…

We construct families of smooth affine surfaces with pairwise non isomorphic A 1-cylinders but whose A 2-cylinders are all isomorphic. These arise as complements of cuspidal hyperplane sections of smooth projective cubic surfaces.

In characteristic $p>0$ and for $q$ a power of $p$, we compute the number of nonplanar rational curves of arbitrary degrees on a smooth Hermitian surface of degree $q+1$ under the assumption that the curves have a parametrization given by…

We prove that the space of affine, transversal at infinity, non-singular real cubic surfaces has 15 connected components. We give a topological criterion to distinguish them and show also how these 15 components are adjacent to each other…

We construct the first examples of rationally convex surfaces in the complex plane with hyperbolic complex tangencies. In fact, we give two very different types of rationally convex surfaces: those that admit analytic fillings by…

It is proved that the number of deformation types of complex structures on a fixed oriented smooth four-manifold can be arbitrarily large. The considered examples are locally simple abelian covers of rational surfaces.

We show that a real rational (over $\C$) surfaces are quasi-simple, i.e., that such a surface is determined up to deformation in the class of real surfaces by the topological type of its real structure.

We show that there is a smooth complex projective variety, of any dimension greater than or equal to two, whose automorphism group is discrete and not finitely generated. Moreover, this variety admits infinitely many real forms which are…

The purpose of this note is to give a short, selfcontained proof of the following result: A complex surface which is diffeomeorphic to a rational surface is rational.

We consider singular holomorphic foliations on compact complex surfaces with invariant rational nodal curve of positive self-intersection. Then, under some assumptions, we list all possible foliations.

We prove that there exist rational but not uniformly rational smooth algebraic varieties. The proof is based on computing a certain numerical obstruction developed in the case of compactifications of affine spaces. We show that for some…

We construct smooth rational real algebraic varieties of every dimension $\ge$ 4 which admit infinitely many pairwise non-isomorphic real forms.

We construct a projective variety with discrete, non-finitely generated automorphism group. As an application, we show that there exists a complex projective variety with infinitely many non-isomorphic real forms.

We prove that the Cox ring of a smooth rational surface with big anticanonical class is finitely generated. We classify surfaces of this type that are blow-ups of the plane at distinct points lying on a (possibly reducible) cubic.