论文标题
稳定的半三相不可分解的品种
Stably semiorthogonally indecomposable varieties
论文作者
论文摘要
如果三角类别不承认非平凡的半三相分解，则据说它是不可分解的。我们介绍了非共同稳定的半三相不可分解（NSSI）品种的定义。该提议意味着，除其他外，每个平滑的亚属变量都具有不可分解的衍生类别的连贯滑轮类别，如果$ y $是nssi，那么对于任何品种$ x $，所有半超声分解为$ x \ times y $都是$ x $的分解。我们证明，任何阿尔巴尼人形态为有限的品种都是NSSI，并且NSSI纤维在NSSI底座上的振动总空间也是NSSI。我们应用这种不可塑性，以推断出某些品种中没有幻影子类别，包括表面$ c \ times \ times \ mathbb {p}^1 $，其中$ c $是阳性属的任何平滑曲线。
A triangulated category is said to be indecomposable if it admits no nontrivial semiorthogonal decompositions. We introduce a definition of a noncommutatively stably semiorthogonally indecomposable (NSSI) variety. This propery implies, among other things, that each smooth proper subvariety has indecomposable derived category of coherent sheaves, and that if $Y$ is NSSI, then for any variety $X$ all semiorthogonal decompositions of $X \times Y$ are induced from decompositions of $X$. We prove that any variety whose Albanese morphism is finite is NSSI, and that the total space of a fibration over NSSI base with NSSI fibers is also NSSI. We apply this indecomposability to deduce that there are no phantom subcategories in some varieties, including surfaces $C \times \mathbb{P}^1$, where $C$ is any smooth proper curve of positive genus.
