Quintic genus 2 curves, stable pairs and wall-crossing

Abstract: This paper studies wall crossings in Bridgeland stability for the moduli space of Pandharipande--Thomas stable pairs associated with quintic genus 2 curves in the complex projective three-space. We provide a complete list of irreducible components of the moduli space, together with a birational description of each component. As an application, we recover the geometry of the Hilbert scheme for quintic genus 2 curves, for which no previous results are known.