On the gonality of curves in Pn
نویسنده
چکیده
Here we study the gonality of several projective curves which arise in a natural way (e.g. curves with maximal genus in Pn, curves with given degree d and genus g for all possible d, g if n = 3 and with large g for arbitrary (d, g, n)).
منابع مشابه
Clifford Index of Acm Curves in P
In this paper we review the notions of gonality and Clifford index of an abstract curve. For a curve embedded in a projective space, we investigate the connection between the Clifford index of the curve and the geometrical properties of its embedding. In particular if C is a curve of degree d in P 3 , and if L is a multisecant of maximum order k , then the pencil of planes through L cuts out a ...
متن کاملCurves and Line Bundles on Del Pezzo Surfaces
We extend the results of Pareschi [Pa] on the constancy of the gonality and Clifford index of smooth curves in a complete linear system on Del Pezzo surfaces of degrees ≥ 2 to the case of Del Pezzo surfaces of degree 1, where we explicitly classify the cases where the gonality and Clifford index are not constant. We also classify all cases of exceptional curves on Del Pezzo surfaces, which turn...
متن کاملLinear Syzygies of Curves with Prescribed Gonality
We prove two statements concerning the linear strand of the minimal free resolution of a k-gonal curve C of genus g. Firstly, we show that a general curve C of genus g of nonmaximal gonality k ≤ g+1 2 satisfies Schreyer’s Conjecture, that is, bg−k,1(C,KC) = g−k. This is a statement going beyond Green’s Conjecture and predicts that all highest order linear syzygies in the canonical embedding of ...
متن کاملThe Extremal Secant Conjecture for Curves of Arbitrary Gonality
We prove the Green–Lazarsfeld Secant Conjecture [GL1, Conjecture (3.4)] for extremal line bundles on curves of arbitrary gonality, subject to explicit genericity assumptions.
متن کاملThe Tangent Cones at Double points of Prym-Canonical Divisors of Curves of genus 7
Let η be a line bundle on a smooth curve X with η^2=0 such that π_η, the double covering induced by η is an etale morphism. Assume also that X_η be the Prym-canonical model of X associated to K_X.η and Q is a rank 4 quadric containing X_η. After stablishing the projective normality of the prym-canonical models of curves X with Clifford index 2, we obtain in this paper a sufficient condition for...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010