论文标题
球形函数和拖失弗洛普自动等效性
Spherical functors and the flop-flop autoequivalence
论文作者
论文摘要
拖鞋是异性转变，猜想会诱导衍生的等效性。在许多情况下，可以通过分辨率的分辨率将等效产生为拉力。发生这种情况时，我们将具有称为\ emph {flop-flop autoquilence}的拖失侧的两侧的非平凡自动等效性。我们证明，这种自动等效性可以实现为围绕保守的球形函数的球形扭曲的倒数，以自然的方式。更确切地说，我们证明了一个自然的，保守的球形函子存在于更一般的框架中，并且Flop-lop自动等效性适合这张图片。我们还提供了标准拖鞋（本地模型和家庭案例）和Mukai Flops的球形函数源类别的明确描述。我们以一些关于格拉斯曼尼亚拖鞋和阿布夫拖鞋的猜测结束了。
Flops are birational transformations which, conjecturally, induce derived equivalences. In many cases an equivalence can be produced as pull-push via a resolution of the birational transformation; when this happens, we have a non-trivial autoequivalence of either sides of the flop known as the \emph{flop-flop autoequivalence}. We prove that such autoequivalence can be realised as the inverse of a spherical twist around a conservative, spherical functor in a natural way. More precisely, we prove that a natural, conservative spherical functor exists in a more general framework and that the flop-flop autoequivalence fits into this picture. We also give an explicit description of the source category of the spherical functor for standard flops (local model and family case) and Mukai flops. We conclude with some speculation about Grassmannian flops and the Abuaf flop.
