Bridgeland stability conditions and skew lines on $\mathbb{P}^3$

Author:

Sammy Alaoui Soulimani, Martin G. Gulbrandsen

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)

journal:

date:

2023-08-06 16:00:00

Abstract

Inspired by Schmidt's work on twisted cubics, we study wall crossings in Bridgeland stability, starting with the Hilbert scheme $\mathrm{Hilb}^{2m+2}(\mathbb{P}^3)$ 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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