Hilbert scheme of twisted cubics as simple wall-crossing

2016/08/16 by Xia, Bingyu · 2 citations
#14F05 (Primary) #14H45 #14J60 #18E30 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.04609

Abstract

We study the Hilbert scheme of twisted cubics in the three-dimensional projective space by using Bridgeland stability conditions. We use wall-crossing techniques to describe its geometric structure and singularities, which reproves the classical result of Piene and Schlessinger.

Cited by

• Quintic genus 2 curves, stable pairs and wall-crossing
• Some examples of moduli spaces on surfaces via wall-crossing

Related

• Bridgeland stability conditions and skew lines on ℙ³
• Twisted cubics and quadruples of points on cubic surfaces
• Hilbert schemes and stable pairs: GIT and derived category wall crossings
• Wall-crossing structures on surfaces
• Bridgeland walls destabilizing one-dimensional space sheaves