论文标题
超出表面的分类Torelli定理
Categorical Torelli theorem for hypersurfaces
论文作者
论文摘要
令$ x \ subset \ mathbb {p}^{n+1} $为尺寸$ n $和度量$ d $的平滑fano hypersurface。 $ x $上的连贯带束的派生类别包含一个有趣的子类别，称为kuznetsov component $ \ mathcal {a} _x $。我们表明，该子类别以及称为旋转函数的一定自动等效性，如果$ d> 3 $或$ d = 3 $ and $ n> 3 $确定$ x $唯一。这概括了D. Huybrechts和J. Rennemo的结果，他们在额外的假设中证明了相同的说法，即$ d $划分了$ n+2 $。
Let $X \subset \mathbb{P}^{n+1}$ be a smooth Fano hypersurface of dimension $n$ and degree $d$. The derived category of coherent sheaves on $X$ contains an interesting subcategory called the Kuznetsov component $\mathcal{A}_X$. We show that this subcategory, together with a certain autoequivalence called the rotation functor, determines $X$ uniquely if $d > 3$ or if $d = 3$ and $n > 3$. This generalizes a result by D. Huybrechts and J. Rennemo, who proved the same statement under the additional assumption that $d$ divides $n+2$.
