Generalized divisors on Gorenstein curves and a theorem of Noether

Gorenstein Liaison via Divisors

Du Val Curves and the Pointed Brill-noether Theorem

We show that a general curve in an explicit class of what we call Du Val pointed curves satisfies the Brill-Noether Theorem for pointed curves. Furthermore, we prove that a generic pencil of Du Val pointed curves is disjoint from all Brill-Noether divisors on the universal curve. This provides explicit examples of smooth pointed curves of arbitrary genus defined over Q which are Brill-Noether g...

Divisors on Nonsingular Curves

In the case that X,Y are projective, nonsingular curves and φ is nonconstant, we already know that φ is necessarily surjective, but we will prove (more accurately, sketch a proof of) a much stronger result. From now on, for convenience, when we speak of the local ring of a nonsingular curve as being a discrete valuation ring, we assume that the valuation is normalized so that there is an elemen...

Divisors on real curves

Let X be a smooth projective curve over R. In the first part, we study e¤ective divisors on X with totally real or totally complex support. We give some numerical conditions for a linear system to contain such a divisor. In the second part, we describe the special linear systems on a real hyperelliptic curve and prove a new Cli¤ord inequality for such curves. Finally, we study the existence of ...

On Néron Models, Divisors and Modular Curves

For p a prime number, let X0(p)Q be the modular curve, over Q, parametrizing isogenies of degree p between elliptic curves, and let J0(p)Q be its jacobian variety. Let f : X0(p)Q → J0(p)Q be the morphism of varieties over Q that sends a point P to the class of the divisor P − ∞, where ∞ is the Q-valued point of X0(p)Q that corresponds to PQ with 0 and ∞ identified, equipped with the subgroup sc...