Related papers: $G$-solid Rational Surfaces
We classify smooth projective surfaces that are quotients of abelian surfaces by finite groups.
We propose and compare various techiques available to produce smooth cubic hypersurfaces over a non-algebraically-closed field which have rational points but which are not stably rational over their ground field.
We prove the rationality of the coarse moduli spaces of Coble surfaces and of nodal Enriques surfaces over the field of complex numbers.
Let $\Bbbk$ be any field of characteristic zero, $X$ be a cubic surface in $\mathbb{P}^3_{\Bbbk}$ and $G$ be a group acting on $X$. We show that if $X(\Bbbk) \ne \varnothing$ and $G$ is not trivial and not a group of order $3$ acting in a…
The families of smooth rational surfaces in $\PP^4$ have been classified in degree $\le 10$. All known rational surfaces in $\PP^4$ can be represented as blow-ups of the plane $\PP^2$. The fine classification of these surfaces consists of…
One of the most powerful ideas in the study and classification of algebraic varieties is the notion of a model: that is, to single out an object, in the appropriate isomorphism class, with nice properties. This survey aims to define and…
By the famous ADE classification rational double points are simple. Rational triple points are also simple. We conjecture that the simple normal surface singularities are exactly those rational singularities, whose resolution graph can be…
We describe smooth rational projective algebraic surfaces over an algebraically closed field of characteristic different from 2 which contain $n \ge \b_2-2$ disjoint smooth rational curves with self-intersection -2, where $\b_2$ is the…
We prove that any smooth cubic surface defined over any number field satisfies the lower bound predicted by Manin's conjecture possibly after an extension of small degree.
A general type of ray class fields of global function fields is investigated. The systematic computation of their genera leads to new examples of curves over finite fields with comparatively many rational points.
We classify all complex surfaces with quotient singularities that do not contain any smooth rational curves, under the assumption that the canonical divisor of the surface is not pseudo-effective. As a corollary we show that if $X$ is a log…
A determination of the fixed components, base points and irregularity is made for arbitrary numerically effective divisors on any smooth projective rational surface having an effective anticanonical divisor. All of the results are proven…
In this paper the log surfaces without $\QQ$-complement are classified. In particular, they are non-rational always. This result takes off the restriction in the theory of complements and allows one to apply it in the most wide class of log…
A K3 surface over a number field has infinitely many rational points over a finite field extension. For K3 surfaces of degree 2, arising as double covers of $\mathbb{P}^2$ branched along a smooth sextic curve, we give a bound for the degree…
We study rationality properties of real singular cubic threefolds.
We classify surfaces of general type whose bicanonical map is composed with a rational map of degree 2 onto a rational or ruled surface.
Let $\Gamma_g$ be the fundamental group of a closed connected orientable surface of genus $g\geq2$. We introduce a combinatorial structure of "core surfaces", that represent subgroups of $\Gamma_g$. These structures are (usually)…
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 determine the rational divisor class group of the moduli spaces of smooth pointed hyperelliptic curves and of their Deligne-Mumford compactification, over the field of complex numbers.
We prove that the Euler-Chow series for ruled surfaces and scrolls is rational by means of an explicit computation.