Related papers: Degree-2 Abel maps for nodal curves
In this paper we obtain an explicit formula for the number of curves in two dimensional complex projective space, of degree d, passing through d(d+3)/2-(k+1) generic points and having one node and one codimension k singularity, where k is…
A set of nodes is called $n$-independent if each its node has a fundamental polynomial of degree $n.$ We proved in a previous paper [H. Hakopian and S. Toroyan, On the minimal number of nodes determining uniquelly algebraic curves, accepted…
We study locally Cohen-Macaulay curves in projective three-space which are contained in a double plane 2H, thus completing the classification of curves lying on surfaces of degree two. We describe the irreducible components of the Hilbert…
In the first part, we introduce a notion a degree of edge-colorings of bicubic plane graphs and proves some local formula of the graded number of colorings. In the second part, we give a new proof of a result of Fisk saying that any two…
Recently, there has been great interest in the application of composition laws to problems in enumerative geometry. Using the moduli space of stable maps, we compute the number of irreducible, reduced, nodal, degree-$d$ genus-$2$ plane…
The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this geometrical description is less trivial, it can be…
We classify surjective self-maps (of degree at least two) of affine surfaces according to the log Kodaira dimension.
An analytic approach and description are presented for the moduli cotangent sheaf for suitable stable curve families including noded fibers. For sections of the square of the relative dualizing sheaf, the residue map at a node gives rise to…
We give some new congruences for singular real algebraic curves which generalize Fiedler's congruence for nonsingular curves.
In this paper, we study maps from reducible curves $f : C \cup_\Gamma D \to \mathbb{P}^r$. We restrict our attention to two cases: first, when $f|_D$ factors through a hyperplane $H$ and $f|_C$ is transverse to $H$; and second, when $r =…
We survey the theory of the compactified Jacobian associated to a singular curve. We focus on describing low genus examples using the Abel map.
We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense.…
We consider systems of simple closed curves on surfaces and their total number of intersection points, their so-called crossing number. For a fixed number of curves, we aim to minimise the crossing number. We determine the minimal crossing…
We prove the Dynamical Andr\'e-Oort (DAO) conjecture proposed by Baker and DeMarco for families of rational maps parameterized by an algebraic curve. In fact, we prove a stronger result, which is a Bogomolov type generalization of DAO for…
We prove Goh conditions of order n for strictly singular length minimizing curves of corank 1, under the assumption that the lower order intrinsic differentials of the end-point map vanish. This result relies upon the proof of an open…
We introduce and begin the topological study of real rational plane curves, all of whose inflection points are real. The existence of such curves is a corollary of results in the real Schubert calculus, and their study has consequences for…
New invariants for 2-dimensional cell complexes are defined, which can be interpreted as curvature bounds. These invariants are proved to be rational and computable in a companion article. This document is a survey that collects theorems…
In this paper we present several formulae for computing the partial degrees of the defining polynomial of the offset curve to an irreducible affine plane curve given implicitly, and we see how these formulae particularize to the case of…
We describe the topology of singular real algebraic curves in a smooth surface. We enumerate and bound in terms of the degree the number of topological types of singular algebraic curves in the real projective plane.
We show that after mapping each element of a set of second class constraints to the surface of the other ones, half of them form a subset of abelian first class constraints. The explicit form of the map is obtained considering the most…