Related papers: Monodromy of Projective Curves

The main purpose of this paper is to provide a structure theorem for codimension one singular transversely projective foliationson projective manifolds. To reach our goal, we firstly extend Corlette-Simpson's classification of rank two…

The general problem which initiated this work is: What are the quasiprojective varieties which can be uniformized by means of bounded domains in $\cz^n$ ? Such a variety should be, in particular, C--hyperbolic, i.e. it should have a…

We develop a framework for characterizing isometric immersions of simply connected, bounded, planar regions with piecewise smooth boundaries into three-dimensional space. Each immersion is associated with a framed curve along the boundary…

A linear system of plane curves satisfying multiplicity conditions at points in general position is called special if the dimension is larger than the expected dimension. A (-1) curve is an irreducible curve with self intersection -1 and…

Consider the smooth projective models C of curves y^2=f(x) with f(x) in Z[x] monic and separable of degree 2g+1. We prove that for g >= 3, a positive fraction of these have only one rational point, the point at infinity. We prove a lower…

We prove a version of Bourgain's projection theorem for parametrized families of $C^2$ maps, that refines the original statement even in the linear case. As one application, we show that if $A$ is a Borel set of Hausdorff dimension close to…

We study the Tannakian properties of the category of perverse sheaves on elliptic curves endowed with the convolution product. We establish that for certain sheaves with unipotent local monodromy over seven points the corresponding Tannaka…

Let $D$ be a non-pseudoconvex open set in $\C^3$ and $S$ be the union of all two-dimensional planes with non-empty and non-pseudoconvex intersection with $D.$ Sufficient conditions are given for $\C^3\setminus S$ to belong to a complex…

We study "pure-cycle" Hurwitz spaces, parametrizing covers of the projective line having only one ramified point over each branch point. We start with the case of genus-0 covers, using a combination of limit linear series theory and group…

In this paper we prove that, for any $n\ge 3$, there exist infinitely many $r\in \N$ and for each of them a smooth, connected curve $C_r$ in $\P^r$ such that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme…

We prove here the following results: \begin{th} Let $E$ a rank 2 vector bundle over ${\bf P}_3$, if $C$ is a reduced irreducible curve of ${\bf P}_3^{\vee}$ such that $E_H$ is unstable for all $H\in C$ then $C$ is a line. \end{th} We define…

This paper contains results on stable bundles of rank 2 with space of sections of dimension 4 on a smooth irreducible projective algebraic curve $C$. There is a known lower bound on the degree for the existence of such bundles; the main…

Let $\mathcal{C}$ be an irreducible plane curve of $\text{PG}(2,\mathbb{K})$ where $\mathbb{K}$ is an algebraically closed field of characteristic $p\geq 0$. A point $Q\in \mathcal{C}$ is an inner Galois point for $\mathcal{C}$ if the…

We consider Marstrand type projection theorems for closest-point projections in the normed space $\mathbb{R}^2$. We prove that if a norm on $\mathbb{R}^2$ is regular enough, then the analogues of the well-known statements from the Euclidean…

In this article we exhibit certain projective degenerations of smooth $K3$ surfaces of degree $2g-2$ in $\Bbb P^g$ (whose Picard group is generated by the hyperplane class), to a union of two rational normal scrolls, and also to a union of…

Given a family of cyclic covers of $\mathbb{P}^1$ and a prime $p$ of good reduction, by [12] the generic Newton polygon (resp. Ekedahl--Oort type) in the family ($\mu$-ordinary) is known. In this paper, we investigate the existence of…

Let $Y$ be an $(m+1)$-dimensional irreducible smooth complex projective variety embedded in a projective space. Let $Z$ be a closed subscheme of $Y$, and $\delta$ be a positive integer such that $\mathcal I_{Z,Y}(\delta)$ is generated by…

Let $X$ be a geometrically irreducible smooth projective curve defined over a field $k$. Assume that $X$ has a $k$-rational point; fix a $k$-rational point $x\in X$. From these data we construct an affine group scheme ${\mathcal G}_X$…

We first describe the local and global moduli spaces of germs of foliations defined by analytic functions in two variables with p transverse smooth branches, and with integral multiplicities (in the univalued holomorphic case) or complex…

A Riemannian manifold is said to be almost positively curved if the sets of points for which all $2$-planes have positive sectional curvature is open and dense. We show that the Grassmannian of oriented $2$-planes in $\mathbb{R}^7$ admits a…