AI 中文总结
本文研究三次七重流形的库兹涅佐夫分量，构造了光滑情形下该分量到克利福德模导出范畴的嵌入，以及沿直线奇异的一般情形下其弱平繁范畴消解，得到了Favero-Kelly的结果。
AI 中文摘要
设$Y$为三次七重流形。当$Y$光滑时，其库兹涅佐夫分量是3维卡拉比-丘范畴，我们构造了该库兹涅佐夫分量到$\boldsymbol{P}^4$上克利福德模的导出范畴的嵌入。当$Y$是沿一条直线奇异的一般三次七重流形时，我们通过光滑卡拉比-丘3维流形的导出范畴构造了其库兹涅佐夫分量的显式弱平繁范畴消解，得到了Favero-Kelly的结果。在该构造中，我们将消解函子显式表示为几何函子与突变的复合，并将其核确定为等价于栈曲线导出范畴拉回的范畴。
英文摘要
Let $Y$ be a cubic 7-fold. When $Y$ is smooth, its Kuznetsov component is a Calabi-Yau category of dimension 3, and we construct an embedding of the Kuznetsov component into the derived category of Clifford modules over $\mathbb{P}^4$. When $Y$ is a general cubic 7-fold singular along a line, we construct an explicit weakly crepant categorical resolution of its Kuznetsov component by the derived category of a smooth Calabi-Yau 3-fold, recovering a result of Favero-Kelly. In this construction, we express the resolution functor explicitly as a composition of geometric functors and mutations, and identify its kernel with a category equivalent to a pull-back of the derived category of a stacky curve.
Comments23 pages, 5 figures. Comments are welcome
