Year: 2022
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Sung, Benjamin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4306800978