Quintic genus 2 curves, stable pairs and wall-crossing

2025/09/24 by Ma, Shihao, Yang, Song
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.20076

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.

Citations

• Bridgeland stability conditions and skew lines on ℙ³
• An interesting wall-crossing: Failure of the wall-crossing/MMP correspondence
• Hilbert scheme of twisted cubics as simple wall-crossing
• Stability conditions on Fano threefolds of Picard number one
• Moduli of Bridgeland semistable objects on 3-folds and Donaldson-Thomas invariants
• The Space of Stability Conditions on Abelian Threefolds, and on some\n Calabi-Yau Threefolds
• Moduli of sheaves supported on quartic space curves
• Bridgeland Stability conditions on threefolds I: Bogomolov-Gieseker type inequalities
• Curve counting theories via stable objects I. DT/PT correspondence
• Stability conditions on K3 surfaces
• Stability conditions on triangulated categories
• On the moduli scheme of stable sheaves supported on cubic space curves

Related

• Geometry of canonical genus four curves
• Moduli of Genus Six Curves and K-stability
• Hilbert schemes and stable pairs: GIT and derived category wall crossings
• Moduli Spaces of α-stable Pairs and Wall-Crossing on ℙ²
• Bridgeland stability conditions and skew lines on ℙ³