Remarks on the Gieseker-Petri divisor in genus eight

In the moduli space of curves of genus 8, M ₈, denote by GP ₈ the locus of curves that do not satisfy the Gieseker-Petri theorem. In this short note we study the projective plane models of curves of genus 8 that do not satisfy the Gieseker-Petri theorem. We use these projective models to exhibit an irreducible divisorial component in GP ₈ and we show that GP ₈ is an irreducible divisor.