Perverse schobers are categorical analogs of perverse sheaves. Examples arise from varieties admitting flops, determined by diagrams of derived categories of coherent sheaves associated to the flop: in this paper we construct mirror partners to such schobers, determined by diagrams of Fukaya categories with stops, for examples in dimensions 2 and 3. Interpreting these schobers as supported on loci in mirror moduli spaces, we prove homological mirror symmetry equivalences between them. Our construction uses the coherent–constructible correspondence and a recent result of Ganatra et al. (Microlocal morse theory of wrapped fukaya categories. arXiv:1809.08807 ) to relate the schobers to certain categories of constructible sheaves. As an application, we obtain new mirror symmetry proofs for singular varieties associated to our examples, by evaluating the categorified cohomology operators of Bondal et al. (Selecta Math 24 (1):85–143, 2018) on our mirror schobers.

中文翻译：

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来自双有理几何的 Perverse Schobers 的镜像对称

Perverse schobers 是 perverse sheaves 的绝对类比。例子来自允许 flop 的变体，由与 flop 相关联的相干滑轮的派生类别图确定：在本文中，我们构建了这种 schober 的镜像伙伴，由带有停止的 Fukaya 类别图确定，例如维度 2 和 3。这些 schober 在镜像模空间中的轨迹上得到支持，我们证明了它们之间的同调镜像对称等价。我们的构造使用了连贯-可构造的对应关系和 Ganatra 等人的最新结果。（包裹深谷类别的微局域莫尔斯理论。arXiv：1809.08807）将 schober 与某些类别的可构造滑轮联系起来。作为一个应用，我们获得了与我们的例子相关的奇异变体的新镜像对称证明，通过评估 Bondal 等人的分类上同调算子。（Selecta Math 24 (1):85–143, 2018）在我们的镜子 schobers 上。