论文标题
非交通曲线的稳定条件
Stability conditions on non-commutative curves
论文作者
论文摘要
我们证明，任何具有尺寸的Bridgeland稳定性条件小于$ \ frac {6} {5} $的非交换光滑投射变体都必须是平滑的投影曲线。结果，我们在间隔$（1，\ frac {6} {5}）$中推断出具有维度的此类类别的不存在。此外，我们证明了使用稳定物体的模量$ 1 $ 1 $的稳定物体的模量空间，这是较高属的光滑射击曲线的急剧重建结果，并推断出其半正相分解的结构性结果。
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.
