Bridgeland stability conditions and skew lines on ℙ³

2023/08/07 by Soulimani, Sammy Alaoui, Gulbrandsen, Martin G. · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.03820

Abstract

Inspired by Schmidt's work on twisted cubics, we study wall crossings in Bridgeland stability, starting with the Hilbert scheme Hilb^2m+2(ℙ³) parametrizing pairs of skew lines and plane conics union a point. We find two walls. Each wall crossing corresponds to a contraction of a divisor in the moduli space and the contracted space remains smooth. Building on work by Chen--Coskun--Nollet we moreover prove that the contractions are K-negative extremal in the sense of Mori theory and so the moduli spaces are projective.

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• Quintic genus 2 curves, stable pairs and wall-crossing

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