Brill-Noether with ramification at unassigned points

TL;DR

This paper presents a solution to the Brill-Noether problem concerning the nonexistence of linear series with specified ramification at unassigned points on moduli spaces of pointed curves, using foundational divisor facts.

Contribution

It introduces a novel approach leveraging divisor properties on moduli spaces to address the Brill-Noether problem for unassigned points.

Findings

Provides a new proof for the nonexistence of certain linear series

Utilizes divisor theory on moduli spaces of pointed curves

Simplifies the understanding of ramification conditions in Brill-Noether theory

Abstract

We discuss in this short note how basic facts about divisors on moduli spaces of pointed curves give a solution to the Brill-Noether problem of nonexistence of linear series with prescribed ramification at unassigned points.