Related papers: Ramification divisors of general projections

Suppose that $C\subset\mathbb P^2$ is a general enough nodal plane curve of degree $>2$, $\nu\colon \hat C\to C$ is its normalization, and $\pi\colon \hat C\to\mathbb P^1$ is a finite morphism simply ramified over the same set of points as…

This paper investigates the stratification of the discriminant hypersurface associated with a univariate polynomial via the number of its distinct complex roots. We introduce two novel approaches different from the one based on…

We study some integral model of P.E.L. Shimura varieties of type A for ramified primes. Precisely, we look at the Pappas-Rapoport model (or splitting model) of some unitary Shimura varieties for which there is ramification in the degree 2…

The main result is a wall crossing formula for central projections defined on submanifolds of a real projective space. Our formula gives the jump of the degree of such a projection when the center of the projection varies. The fact that the…

Consider the scheme parametrizing non-constant morphisms from a fixed projective curve to a projective surface. There is a rational map between this scheme and the Chow variety of $1$-cycles on the surface. We prove that, if the curve is…

In this paper we introduce the notion of rational Hausdorff divisor, we analyze the dimension and irreducibility of its associated linear system of curves, and we prove that all irreducible real curves belonging to the linear system are…

In this article we present a unified way to smooth certain multiple structures called ropes on smooth varieties. We prove that most ropes of arbitrary multiplicity, supported on smooth curves can be smoothed. By a rope being smoothable we…

For a constructible \'etale sheaf on a smooth variety of positive characteristic ramified along an effective divisor, the largest slope in Abbes and Saito's ramification theory of the sheaf gives a divisor with rational coefficients called…

We study extremality properties of covering families of rational curves on projective varieties. Among others, we show that on a normal and Q-factorial projective variety of dimension at most 4, every covering and quasi-unsplit family of…

In continuation of our work in Comm. in Algebra, vol. 28 (2000), we study ramified coverings of projective manifolds, in particular over Fano manifolds and investigate positivity properties of the associated vector bundle. Moreover we study…

The theory of Q-Cartier divisors on the space of n-pointed, genus 0, stable maps to projective space is considered. Generators and Picard numbers are computed. A recursive algorithm computing all top intersection products of Q-Divisors is…

We study projective surfaces $X \subset \mathbb{P}^r$ (with $r \geq 5$) of maximal sectional regularity and degree $d > r$, hence surfaces for which the Castelnuovo-Mumford regularity $\reg(\mathcal{C})$ of a general hyperplane section…

In this paper, we give a simple description of the deformations of a map between two smooth curves with partially prescribed branching, in the cases that both curves are fixed, and that the source is allowed to vary. Both descriptions work…

The aim of this paper is to present an algebro-geometric approach to the study of the geometry of the moduli space of stable bundles on a smooth projective curve defined over an algebraically closed field $k$, of arbitrary characteristic.…

We prove that the ramified Prym map $\mathcal P_{g, r}$ which sends a covering $\pi:D\longrightarrow C$ ramified in $r$ points to the Prym variety $P(\pi):=\text{Ker}(\text{Nm}_{\pi})$ is an embedding for all $r\ge 6$ and for all $g(C)>0$.…

We solve the equivalence problem for rank 3 completely nonholonomic vector distributions with 6-dimensional square on a smooth manifold of arbitrary dimension n under very mild genericity conditions. The main idea is to consider the…

The philosophy that ``a projective manifold is more special than any of its smooth hyperplane sections" was one of the classical principles of projective geometry. Lefschetz type results and related vanishing theorems were among the…

Let $L/K$ be an extension of number fields that is ramified above $p$. We give a new obstruction to the descent to $K$ of smooth projective varieties defined over $L$. The obstruction is a matrix of $p$-adic numbers that we call ``ramified…

We introduce the notion of log-Riemann surfaces. These are Riemann surfaces given by cutting and pasting planes together isometrically, and come equipped with a holomorphic local diffeomorphism to C called the projection map, and a…

In this paper, we study the geometry of trisections on certain rational elliptic surfaces. We utilize Mumford representations of semi-reduced divisors in order to construct trisections and related plane curves with interesting properties…