Base-point-free Pencils on Triple Covers of Smooth Curves
نویسنده
چکیده
Let X be a smooth algebraic curve. Suppose that there exists a triple covering f : X → Y where Y is a smooth algebraic curve. In this paper, we investigate the existence of morphisms from X to the projective line P which do not factor through the covering f . For this purpose, we generalize the classical results of Maroni concerning base-point-free pencils on trigonal curves to the case of triple covers of arbitrary smooth irrational curves.
منابع مشابه
Fibers of Pencils of Curves on Smooth Surfaces
Let X be a smooth projective surface such that linear and numerical equivalence of divisors on X coincide and let σ ⊆ |D| be a linear pencil on X with integral general fibers. A fiber of σ will be called special if either it is not integral or it has non-generic multiplicity at some of the base points (including the infinitely near ones) of the pencil. In this note we provide an algorithm to co...
متن کاملOn the determination of eigenvalues for differential pencils with the turning point
In this paper, we investigatethe boundary value problem for differential pencils on the half-linewith a turning point. Using a fundamental system of solutions, wegive a asymptotic distribution of eigenvalues.
متن کاملOne-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes
We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...
متن کاملOn Green and Green-lazarfeld Conjectures for Simple Coverings of Algebraic Curves
Let X be a smooth genus g curve equipped with a simple morphism f : X → C, where C is either the projective line or more generally any smooth curve whose gonality is computed by finitely many pencils. Here we apply a method developed by Aprodu to prove that if g is big enough then X satisfies both Green and Green-Lazarsfeld conjectures. We also partially address the case in which the gonality o...
متن کاملOn a Finite Type Invariant Giving Complete Classification of Curves on Surfaces
In this paper, we construct a complete invariant for stably homeomorphic classes of curves on compact oriented surfaces without boundaries and show that this is a finite type invariant for curves. In knot theory, it is still unknown whether finite type invariants completely classify knots (the Vassiliev conjecture). We consider the analogy to this conjecture for generic immersed curves: do fini...
متن کامل