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arXiv · 2108.09155

Spherical objects and stability conditions on 2-Calabi--Yau quiver categories

Asilata Bapat·Anand Deopurkar·Anthony M. Licata
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Abstract

Consider a 2-Calabi--Yau triangulated category with a Bridgeland stability condition. We devise an effective procedure to reduce the phase spread of an object by applying spherical twists. Using this, we give new proofs of the following theorems for 2-Calabi--Yau categories associated to ADE quivers: (1) all spherical objects lie in a single orbit of the braid group, and (2) the space of Bridgeland stability conditions is connected.

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Asilata Bapat, Anand Deopurkar, Anthony M. Licata. 2021-08-20. Spherical objects and stability conditions on 2-Calabi--Yau quiver categories. https://arxiv.org/abs/2108.09155

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