论文标题
CDGAS的窗户
Windows for cdgas
论文作者
论文摘要
我们研究了与任何领域上任意奇异（不一定会减少或不可减少）仿生的傅立叶核相关的。该内核与用于墙壁交叉的衍生纤维产物图密切相关，并且从交换差分级代数的角度易于理解。但是，从代数品种的角度来看，内核可能非常复杂，对应于具有多个同源性滑轮的复合物。在Calabi-yau案中的轻度假设下，我们证明该内核在两个GIT商上的完美复合物类别之间提供了等效性。更普遍地，我们获得了半正交分解，这些分解表明这些类别因派生固定基因座的派生类别的一定数量副本而不同。将Mukai失败的派生等效性回收为非常特殊的情况。
We study a Fourier-Mukai kernel associated to a GIT wall-crossing for arbitrarily singular (not necessarily reduced or irreducible) affine varieties over any field. This kernel is closely related to a derived fiber product diagram for the wall-crossing and simple to understand from the viewpoint of commutative differential graded algebras. However, from the perspective of algebraic varieties, the kernel can be quite complicated, corresponding to a complex with multiple homology sheaves. Under mild assumptions in the Calabi-Yau case, we prove that this kernel provides an equivalence between the category of perfect complexes on the two GIT quotients. More generally, we obtain semi-orthogonal decompositions which show that these categories differ by a certain number of copies of the derived category of the derived fixed locus. The derived equivalence for the Mukai flop is recovered as a very special case.
