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arXiv · 2210.08637

Stability conditions on non-commutative curves

Benjamin Sung
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Abstract

We prove that any non-commutative smooth projective variety with a Bridgeland stability condition of dimension less than $\frac{6}{5}$ must be a smooth projective curve. As a consequence, we deduce the non-existence of such categories with dimension in the interval $(1,\frac{6}{5})$. Moreover, we prove a sharp reconstruction result for smooth projective curves of higher genus using the moduli space of stable objects in a category of dimension $1$, and deduce a structural result for their semi-orthogonal decompositions.

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Benjamin Sung. 2022-10-16. Stability conditions on non-commutative curves. https://arxiv.org/abs/2210.08637

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