Related papers: Smooth projective surfaces with infinitely many re…

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…

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…

We classify Enriques surfaces with smooth K3 cover and finite automorphism group in arbitrary positive characteristic. The classification is the same as over the complex numbers except that some types are missing in small characteristics.…

We will show that there is a smooth complex projective surface, birational to some Enriques surface, such that the automorphism group is discrete but not finitely generated.

We exhibit a smooth complex rational affine surface with uncountably many nonisomorphic real forms.

It was proved by Tien-Cuong Dinh and me that there is a smooth complex projective surface whose automorphism group is discrete and not finitely generated. In this paper, we will show that there is a smooth projective surface, birational to…

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 show, among other things, that for each integer $n \ge 3$, there is a smooth complex projective rational variety of dimension $n$, with discrete non-finitely generated automorphism group and with infinitely many mutually non-isomorphic…

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

In this article, we prove that a smooth projective complex surface $X$ which is regular (i.e. such that $h^1(X,\mathcal O_X)=0$) and which has a $\mathbb{R}$-divisor $\Delta$ such that $(X,\Delta)$ is a KLT Calabi-Yau pair has finitely many…

The paper contains a general construction which produces new examples of non simply-connected smooth projective surfaces. We analyze the resulting surfaces and their fundamental groups. Many of these fundamental groups are expected to be…

We prove that, for an Enriques surface in odd characteristic, the automorphism group is finitely generated and it acts on the effective nef cone with a rational polyhedral fundamental domain. We also construct a smooth projective surface in…

A complex compact surface which carries an automorphism of positive topological entropy has been proved by Cantat to be either a torus, a K3 surface, an Enriques surface or a rational surface. Automorphisms of rational surfaces are quite…

This note contains preliminary calculation of topological types or real Enriques surfaces. We realize 59 topological types of real Enriques surfaces (Theorem 6) and show that all other topological types belong to the list of 21 topological…

We shall give, in an optimal form, a sufficient numerical condition for the finiteness of the fundamental group of the smooth locus of a normal K3 surface. We shall moreover prove that, if the normal K3 surface is elliptic and the above…

We investigate when the fundamental group of the smooth part of a K3 surface or Enriques surface with Du Val singularities, is finite. As a corollary we give an effective upper bound for the order of the fundamental group of the smooth part…

We survey some recent progress in the study of algebraic varieties X with log terminal singularities, especially, the uni-ruledness of the smooth locus X^0 of X, the fundamental group of X^0 and the automorphisms group on (smooth or…

Let $X$ be surface with isolated singularities in the complex projective space $P^3$ and let denote $Y$ the smooth part of $X$. In this note we discuss some aspects of the topology of such quasi-projective surfaces $Y$: the fundamental…

Complex Enriques surfaces with a finite group of automorphisms are classified into seven types. In this paper, we determine which types of such Enriques surfaces exist in characteristic 2. In particular we give a one dimensional family of…

Let $f \colon X \to X$ be a surjective endomorphism of a normal projective surface. When $\operatorname{deg} f \geq 2$, applying an (iteration of) $f$-equivariant minimal model program (EMMP), we determine the geometric structure of $X$.…