Contents Online
Mathematical Research Letters
Volume 27 (2020)
Number 4
Stability conditions and exceptional objects in triangulated categories
Pages: 945 – 971
DOI: https://dx.doi.org/10.4310/MRL.2020.v27.n4.a1
Author
Abstract
The goal of this paper is to study the subspace of stability condition $\mathcal{E} \subset \operatorname{Stab}(X)$ associated to an exceptional collection $\mathcal{E}$ on a projective variety $X$. Following Macrì’s approach, we show a certain correspondence between the homotopy class of continuous loops in $\Sigma_\mathcal{E}$ and words of the braid group. In particular, we prove that in the case $X = \mathbb{P}^3$ and $\mathcal{E} = \lbrace \mathcal{O},\mathcal{O}(1), \mathcal{O}(2), \mathcal{O}(3) \rbrace$, the space $\Sigma_\mathcal{E}$ is a connected and simply connected $4$-dimensional complex manifold.
Received 8 October 2018
Accepted 20 January 2019
Published 14 December 2020