The Gieseker-Petri divisor in M_g for genus g<=13

TL;DR

This paper proves that the Gieseker-Petri locus is a divisor in the moduli space of curves for genera up to 13, confirming a conjecture about its codimension.

Contribution

It establishes that the Gieseker-Petri locus has pure codimension one in M_g for all g ≤ 13, advancing understanding of its geometric structure.

Findings

GP_g is a divisor in M_g for g ≤ 13

Confirmed the conjecture on the codimension of GP_g

Provides new insights into the geometry of moduli spaces

Abstract

The Gieseker-Petri locus GP_g is defined as the locus inside M_g consisting of curves which violate the Gieseker-Petri Theorem. It is known that GP_g has always some divisorial components and it has been conjectured that it is of pure codimension 1 inside M_g. We prove that this holds true for genus up to 13.