Related papers: A connected component of the moduli space of surfa…

The moduli space ${\mathcal{M}}_{g}$, of genus $g\geq2$ closed Riemann surfaces, is a complex orbifold of dimension $3(g-1)$ which carries a natural real structure i.e. it admits an anti-holomorphic involution $\sigma$. The involution…

Let $X$ be a minimal surface of general type over an algebraically closed field $\mathbf{k}$ of $\mathrm{char}.(\mathbf{k})=p\ge 0$. If the Albanese morphism $a_X:X\to \mathrm{Alb}_X$ is generically finite onto its image, we formulate a…

Let $X$ be a surface of general type with maximal Albanese dimension over an algebraically closed field of characteristic greater than two: we prove that if $K_X^2<\frac{9}{2}\chi(\mathcal{O}_X)$, one has $K_X^2\geq…

Let $S$ be a regular minimal surface of general type over the field of complex numbers, and $\mathrm{Aut}_\mathbb{Q}(S)$ the subgroup of automorphisms acting trivially on $H^*(S,\mathbb{Q})$. It has been known since twenty years that…

Let $S$ be a closed Riemann surface of genus $g\geq 2$ and let ${\rm Aut}(S)$ be its group of conformal automorphisms. It is well known that if either: (i) ${\rm Aut}(S)$ is trivial or (ii) $S/{\rm Aut}(S)$ is an orbifold of genus zero with…

In a previous paper we classified complete stationary surfaces (i.e. spacelike surfaces with zero mean curvature) in 4-dimensional Lorentz space $\mathbb{R}^4_1$ which are algebraic and with total Gaussian curvature $-\int…

In this paper the ubiquity of the Igusa quartic $B \subset \mathbb P^4$ shows up again, this time related to the Prym map $\mathfrak p : \mathcal R_6 \to \mathcal A_5$. We introduce the moduli space $\mathcal X$ of those quartic threefolds…

Answering a question posed by Enriques, we construct a minimal smooth algebraic surface $S$ of general type over the complex numbers with $K^2 = 45$ and $p_g = 4$, and with birational canonical map. Our surface is a regular (q=0) ball…

We study a family of surfaces of general type with $p_g=q=2$ and $K^2=7$, originally constructed by Cancian and Frapporti by using the Computer Algebra System MAGMA. We provide an alternative, computer-free construction of these surfaces,…

Smooth minimal surfaces of general type with $K^2=1$, $p_g=2$, and $q=0$ constitute a fundamental example in the geography of algebraic surfaces, and the 28-dimensional moduli space $\mathbf{M}$ of their canonical models admits a modular…

P. Ellia and G.Sacchiero have shown that if $S$ is a smooth surface in $\Pn 4$ which is ruled in conics, then $S$ has degree 4 or 5. In this paper we give a proof of this result combining the ideas of Ellia and Sacchiero as they are used in…

We study locally flat, compact, oriented surfaces in $4$-manifolds whose exteriors have infinite cyclic fundamental group. We give algebraic topological criteria for two such surfaces, with the same genus $g$, to be related by an ambient…

We describe the normal stable surfaces with K^2=2p_g-3 and p_g>14 whose only non canonical singularity is a cyclic quotient singularity of type 1/4k(1,2k-1) and the corresponding locus D inside the KSBA moduli space of stable surfaces. More…

In this paper we give the topological classification of real primary Kodaira surfaces and we describe in detail the structure of the corresponding moduli space. One of the main tools is the orbifold fundamental group of a real variety. Our…

Components of the Moduli space of sheaves on a K3 surface are parametrized by a lattice; the (algebraic) Mukai lattice. Isometries of the Mukai lattice often lift to symplectic birational isomorphisms of the collection of components. An…

We study the biregular and birational geometry of degree 6 del Pezzo surfaces with Picard number 1, defined over an arbitrary perfect field. Using Galois cohomology techniques, we obtain an explicit description of cocycles for such surfaces…

Algebraically simply connected surfaces of general type with p_g=q=0 and 1\le K^2\le 4 in positive characteristic (with one exception in K^2=4) are presented by using a Q-Gorenstein smoothing of two-dimensional toric singularities, a…

We construct a surface of general type with canonical map of degree 12 which factors as a triple cover and a bidouble cover of $\mathbb P^2$. We also show the existence of a smooth surface with $q=0,$ $\chi=13$ and $K^2=9\chi$ such that its…

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 a connected properly immersed minimal surface in Euclidean 3-space with infinite symmetry group whose intersection with a ball of radius R is less than 2\piR^2 is a plane, a catenoid or a Scherk singly-periodic minimal…