Brill-Noether loci with ramification at two points

TL;DR

This paper proves the injectivity of the Petri map for linear series with specified ramification at two points on a general curve and describes the structure of these series on chains of elliptic curves.

Contribution

It establishes the injectivity of the Petri map for linear series with ramification at two points and characterizes their components on elliptic curve chains.

Findings

Petri map is injective for general curves with two-point ramification.

Describes components of linear series on chains of elliptic curves.

Provides new insights into the structure of linear series with ramification constraints.

Abstract

We prove the injectivity of the Petri map for linear series on a general curve with given ramification at two generic points. We also describe the components of such a set of linear series on a chain of elliptic curves.