Related papers: Completions of $\C^*$-surfaces
We consider a finite analytic morphism $\varphi =(f,g)$ defined from a complex analytic normal surface $(Z,z)$ to ${\mathbb C}^2$. We describe the topology of the image by $\varphi$ of a reduced curve on $(Z,z)$ by means of iterated pencils…
We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…
In this paper a new intrinsic geometric characterization of the symmetric square of a curve and of the ordinary product of two curves is given. More precisely it is shown that the existence on a surface of general type S of irregularity q…
We compute the rational cohomology of the universal family of smooth cubic surfaces using Vassiliev's method of simplicial resolution. Modulo embedding, the universal family has cohomology isomorphic to that of $\mathbb{P}^2$. A consequence…
Let C be a smooth projective curve over a discretely valued field K, defined by an affine equation f(x,y)=0. We construct a model of C over the ring of integers of K using a toroidal embedding associated to the Newton polygon of f. We show…
The classical Kummer construction attaches to an abelian surface a K3 surface. As Shioda and Katsura showed, this construction breaks down for supersingular abelian surfaces in characteristic two. Replacing supersingular abelian surfaces by…
We consider a $C^{1}$ smooth surface with prescribed $p$(or $H$)-mean curvature in the 3-dimensional Heisenberg group. Assuming only the prescribed $p$-mean curvature $H\in C^{0},$ we show that any characteristic curve is $C^{2}$ smooth and…
We classify maximal quartic generalised projective special real curves up to equivalence. A maximal quartic generalised projective special real curve consists of connected components of the intersection of the hyperbolic points of a quartic…
We describe smooth rational projective algebraic surfaces X, over an algebraically closed field of characteristic different from 2, having an even set of four disjoint (-2)-curves N_1,...,N_4, i.e. such that N_1+...+N_4 is divisible by 2 in…
We develop explicit techniques to investigate algebraic quasi-hyperbolicity of singular surfaces through the constraints imposed by symmetric differentials. We apply these methods to prove that rational curves on Barth's sextic surface,…
A complex surface $S$ is said to be isogenous to a product if $S$ is a quotient $S=(C_1 \times C_2)/G$ where the $C_i$'s are curves of genus at least two, and $G$ is a finite group acting freely on $C_1 \times C_2$. In this paper we…
We prove that a surface of prescribed mean curvature ($H$-surface) with free boundary on a two-dimensional $C^2$-manifold belongs to $C^{1,\frac{1}{2}}$ up to that the boundary, provided it is a-priori continuous. We allow the $H$-surface…
In this note, our aim is to show that families of smooth hypersurfaces of $\mathbb R^{n+1}$ which are all $C^1$--close enough to a fixed compact, embedded one, have uniformly bounded constants in some relevant inequalities for mathematical…
We use the Borisov-Keum equations of a fake projective plane and the Borisov-Yeung equations of the Cartwright-Steger surface to show the existence of a regular surface with canonical map of degree 36 and of an irregular surface with…
Generalizing a classical lemma of Castelnuovo, we characterize rational normal curves (resp. linearly normal elliptic curves) as curves $C\subset \PP^n$ such that the number of linearly independent hypersurfaces $Z\supset C$ of given…
This thesis is devoted to the study of abelian automorphism groups of surfaces and $3$-folds of general type over complex number field $\Bbb C$. We obtain a linear bound in $K^3$ for abelian automorphism groups of $3$-folds of general type…
We give a new criterion for when a resolution of a surface of general type with canonical singularities has big cotangent bundle and a new lower bound for the values of $d$ for which there is a surface with big cotangent bundle that is…
It is constructed a formal normal form, using an iterative normalization procedure, for a large class of Real-Smooth Hypersurfaces in Complex Spaces.
We consider the surface diffusion and Willmore flows acting on a general class of (possibly non-compact) hypersurfaces parameterized over a uniformly regular reference manifold possessing a tubular neighborhood with uniform radius. The…
The aim of this article is to make a first step towards the classification of complex normal affine $\mathbb G_a$-threefolds $X$. We consider the case where the restriction of the quotient morphism $\pi\colon X\to S$ to $\pi^{-1}(S_*)$,…