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arXiv · 2011.15120

An interesting wall-crossing: Failure of the wall-crossing/MMP correspondence

Fatemeh Rezaee
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Abstract

We show that the wall-crossing in Bridgeland stability fails to be detected by the birational geometry of stable sheaves, and vice versa. There is a wall in the stability space of canonical genus four curves which does not induce a step in the Minimal Model Program. More precisely, we give an example of a wall-crossing in $\mathrm{D}^{b}(\mathbb{P}^{3})$ such that: the wall induces a small contraction of the moduli space of stable objects associated to one of the adjacent chambers, but a divisorial contraction to the other. This significantly complicates the overall picture in this correspondence to applications of stability conditions to algebraic geometry.

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Fatemeh Rezaee. 2020-11-30. An interesting wall-crossing: Failure of the wall-crossing/MMP correspondence. https://arxiv.org/abs/2011.15120

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