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

Sammy Alaoui Soulimani; Martin G. Gulbrandsen

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arXiv · 2308.03820

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

Sammy Alaoui Soulimani·Martin G. Gulbrandsen

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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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BibTeX RIS

Sammy Alaoui Soulimani, Martin G. Gulbrandsen. 2023-08-07. Bridgeland stability conditions and skew lines on $\mathbb{P}^3$. https://arxiv.org/abs/2308.03820

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