论文标题
奇异性和变性的分类吸收
Categorical absorptions of singularities and degenerations
论文作者
论文摘要
我们介绍了奇异性的分类吸收的概念：从奇异品种的派生类别中删除的操作，一个负责奇异性的小型可允许的子类别，并留下了平稳而适当的类别。我们（在适当的假设下）对带有孤立普通双点的投影品种$ x $进行分类吸收。我们进一步表明，对于平滑曲线$ b $上的任何平滑$ \ Mathcal {x}/b $ of $ x $，$ x $的派生类别的平滑部分扩展到$ \ mathcal {x} $的纤维中的三角形子类别的平滑而适当的三角形子类别。
We introduce the notion of categorical absorption of singularities: an operation that removes from the derived category of a singular variety a small admissible subcategory responsible for singularity and leaves a smooth and proper category. We construct (under appropriate assumptions) a categorical absorption for a projective variety $X$ with isolated ordinary double points. We further show that for any smoothing $\mathcal{X}/B$ of $X$ over a smooth curve $B$, the smooth part of the derived category of $X$ extends to a smooth and proper over $B$ family of triangulated subcategories in the fibers of $\mathcal{X}$.
