Extremal effective divisors of Brill-Noether and Gieseker-Petri type in $\overline{\mathcal M}_{1,n}$

TL;DR

This paper identifies specific divisors of Brill-Noether and Gieseker-Petri type that generate extremal rays in the effective cone of the moduli space of genus one stable curves with marked points, distinct from previously known extremal rays.

Contribution

It demonstrates that certain Brill-Noether and Gieseker-Petri divisors form new extremal rays in the effective cone of ar{\

Findings

Divisors of Brill-Noether and Gieseker-Petri type span extremal rays.

These extremal rays are different from previously known ones.

The results enhance understanding of the effective cone structure in ar{\

Abstract

We show that certain divisors of Brill-Noether and Gieseker-Petri type span extremal rays of the effective cone in the moduli space of stable genus one curves with $n$ ordered marked points. In particular, they are different from the infinitely many extremal rays found in \cite{ChenCoskun}.