Related papers: An explicit class of Lagrangian surfaces

We study parabolic linear Weingarten surfaces in hyperbolic space $\rlopezh^3$. In particular, we classify two family of parabolic surfaces: surfaces with constant Gaussian curvature and surfaces that satisfy the relation…

In this paper some numerical restrictions for surfaces with an involution are obtained. These formulas are used to study surfaces of general type $S$ with $p_g=q=1$ having an involution $i$ such that $S/i$ is a non-ruled surface and such…

We find normal forms for del Pezzo surfaces of degree $2$ over algebraically closed fields of characteristic $2$. For each normal form, we describe the structure of the group of automorphisms of the surface. In particular, we classify all…

We give a systematic construction of uniruled surfaces in positive characteristic. Using this construction, we find surfaces of general type with non-trivial vector fields, surfaces with arbitrarily non-reduced Picard schemes as well as…

We classify minimal complex surfaces of general type with $p_g=q=3$. More precisely, we show that such a surface is either the symmetric product of a curve of genus 3 or a free $\Z_2-$quotient of the product of a curve of genus 2 and a…

We classify smooth del Pezzo surfaces whose alpha-invariant of Tian is bigger than one.

We shall study minimal complex surfaces with $c^2 = 9$ and $\chi=5$ whose canonical classes are divisible by $3$ in the integral cohomology groups, where $c_1^2$ and $\chi$ denote the first Chern number of an algebraic surface and the Euler…

Lagrangian curves in 4-space entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic…

Motivated by a question by D. Mumford : can a computer classify all surfaces with $p_g = 0$ ? we try to show the complexity of the problem. We restrict it to the classification of the minimal surfaces of general type with $p_g = 0, K^2 = 8$…

We use Galois closures of finite rational maps between complex projective varieties to introduce a new method for producing varieties such that the holomorphic part of the cup product map has non-trivial kernel. We then apply our result to…

We study the extension of a hyperelliptic K3 surface to a Fano 6-fold. This determines a family of surfaces of general type with p_g=1, K^2=2 and hyperelliptic canonical curve, where each surface is a weighted complete intersection inside a…

We study Lagrangian cobordism groups of oriented surfaces of genus greater than two. We compute the immersed oriented Lagrangian cobordism group of these surfaces. We show that a variant of this group, with relations given by unobstructed…

In this article, we investigate some properties of cyclic coverings of complex surfaces of general type branched along smooth curves that are numerically equivalent to a multiple of the canonical class. The main results concern coverings of…

In this short note we prove two theorems, the first one is a sharpening of a result of Lange and Sernesi: the discriminant curve W of a general Abelian surface $A$ endowed with an irreducible polarization $D$ of type $(1,3)$ is an…

Let C be a curve (possibly non reduced or reducible) lying on a smooth algebraic surface. We show that the canonical ring R(C, \omega_C) is generated in degree 1 if C is numerically 4-connected, not hyperelliptic and even (i.e. with K_C of…

We show how to construct infinite families of explicitly determined cubic number fields whose class group has a subgroup isomorphic to $(\mathbb{Z}/2)^8$ using degree $1$ del Pezzo surfaces. We illustrate the method and provide an example…

A new class of examples of surfaces with maximal Picard number is constructed. These carry pencils of genus two or three curves such their Jacobian fibrations are isogenous to fibre products of elliptic modular surfaces.

We study the family of irreducible curves with $\delta$ nodes belonging to a free linear system $|C|$ with smooth general member on a surface $S$ such that $|K_S|$ is ample. Under the assumption that $C$ is numerically equivalent to $pK_S$,…

We study minimal Lagrangian surfaces in the complex hyperbolic quadric. We show that minimality of a Lagrangian surface is characterized by a loop of flat connections, which yields an associated $\mathbb S^1$-family of isometric…

The first published non-trivial examples of algebraic surfaces of general type with maximal Picard number are due to Persson, who constructed surfaces with maximal Picard number on the Noether line $K^2=2\chi-6$ for every admissible pair…