Naoki Koseki, Genki Ouchi
A perverse schober is a categorification of a perverse sheaf proposed by Kapranov--Schechtman. In this paper, we construct examples of perverse schobers on the Riemann sphere, which categorify the intersection complexes of natural local systems arising from the mirror symmetry for Calabi-Yau hypersurfaces. The Orlov equivalence plays a key role for the construction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We suggest a possibility for a categorical generalization of the concept of a perverse sheaf, in which vector spaces are replaced by triangulated categories. We call such hypothetical objects perverse Schobers and consider several examples, giving a natural but ad hoc definition in each case. In the simplest case (perverse sheaves on a disk with one possible singular point) we propose, as a categorical analog, the data of a spherical functor.
Perverse schobers are conjectural categorical analogs of perverse sheaves. We show that such structures appear naturally in Homological Minimal Model Program which studies the effect of birational transformations such as flops, on the coherent derived categories. More precisely, the flop data are analogous to hyperbolic stalks of a perverse sheaf. In the first part of the paper we study schober-type diagrams of categories corresponding to flops of relative dimension 1, in particular we determine the categorical analogs of the (compactly supported) cohomology with coefficients in such schobers.…
Perverse schobers are categorifications of perverse sheaves. We construct a perverse schober on a partial compactification of the stringy Kähler moduli space (SKMS) associated by Halpern-Leistner and Sam to a quasi-symmetric representation X of a reductive group G, extending the local system of triangulated categories established by them. The triangulated categories appearing in our perverse schober are subcategories of the derived category of the quotient stack X/G.
This note studies perverse sheaves of categories, or schobers, on Riemann surfaces, following ideas of Kapranov and Schechtman. For certain wall crossings in geometric invariant theory, I construct a schober on the complex plane, singular at each imaginary integer. I use this to obtain schobers for standard flops: in the 3-fold case, I relate these to a further schober on a partial compactification of a stringy Kaehler moduli space, and suggest an application to mirror symmetry.
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-Pardon-Shende t…
Algebra of the Infrared, secondary polytopes and perverse schobers
本文综述了红外代数与次级多面体理论的关系，探讨了隧穿数据与反常 schobers的联系，并提出了向4维理论及复苏形式体系扩展的研究计划。
We relate the Algebra of the Infrared of Gaiotto-Moore-Witten with the theory of perverse schobers which are (conjectural, in general) categorical analogs of perverse sheaves. A perverse schober on a complex plane C can be seen as an algebraic structure that can encode various categories of D-branes of a 2-dimensional supersymmetric field theory, as well as the interaction (tunnelling) between such categories. We show that many constructions of the Algebra of the Infrared can be developed once we have a schober on C. These constructions can be seen as giving various features of the analog, for…
Perverse Schober Structures for Conifold Degenerations
研究 Calabi-Yau 三维流形的一参数退化，其中心纤维含单个普通双点。通过邻近和消失环形式，构造奇异纤维上的 canonical perverse 对象，其在光滑区域限制为常数 perverse sheaf，并与交集复叠相差一个单个秩一贡献。
Perverse schobers and GKZ systems
本文通过构造schobers范畴化，实现了非共振参数下GKZ超几何系统的范畴化，并描述了相关系统的monodromy。
For a balanced wall crossing in geometric invariant theory, there exist derived equivalences between the corresponding GIT quotients if certain numerical conditions are satisfied. Given such a wall crossing, I construct a perverse sheaf of categories on a disk, singular at a point, with half-monodromies recovering these equivalences, and with behaviour at the singular point controlled by a GIT quotient stack associated to the wall. Taking complexified Grothendieck groups gives a perverse sheaf of vector spaces: I characterise when this is an intersection cohomology complex of a local system on…
Relative Calabi-Yau structures and perverse schobers on surfaces
本文研究了相对Calabi-Yau结构与带有边界的perverse schobers在曲面上的构造，结合Fukaya范畴和表示论的例子，定义了perverse schober的monodromy并证明其局部系统性质。
Microlocal perverse schobers and Radon transform
本文提出微局部perverse schobers的范畴化定义，证明其在Radon变换下对曲线$y^m=x^n$不变，并关联Fourier变换、周期SODs与球面单子。
Perverse schobers, stability conditions and quadratic differentials I
本文提出统一方法，通过偏执sheber和正弧系统套件识别来自加权标记表面的三角范畴稳定性条件空间，将混合角化及其翻转与有限长度心和倾斜联系起来。
Betti Tate's thesis and the trace of perverse schobers
本文提出关于反常 schobers 2-范畴的范畴迹猜想，通过证明 Tate 论文的 Betti 几何版本并结合 3d 镜像对称与谱迹结果，在最简单情形下确立了该猜想。
Finite-Node Perverse Schobers and Corrected Extensions for Conifold Degenerations
本文研究具有有限普通双点的单参数 Conifold 褶皱，提出有限节点 bulk/localized-sector 形式化框架，识别修正有限节点 perverse 扩展的第一层范畴结构，并构建混合 Hodge 模包。
Perverse schober defined by Kapranov--Schechtman is a categorification of the notion of perverse sheaf. In their definition, a key ingredient is certain purity property of perverse sheaves. In this short note, we attempt to describe a real analogue of the above story, as categorification of Legendrian points/knots. The notion turns out to include various notions such as semi-orthogonal decomposition, mutation braiding, spherical functor, N-spherical functor, and irregular perverse schober.
Perverse schobers and 3d mirror symmetry
本文将阿贝尔三维镜像对称表述为Gale对偶环面余切栈导出的两类2-范畴之间的等价，给出球面函子2-范畴的谱描述，并建立稳定无穷范畴Smith理想理论与充实无穷范畴双手性结果。
We develop the theory of semi-orthogonal decompositions and spherical functors in the framework of stable $\infty$-categories. Building on this, we study the relative Waldhausen S-construction $S_\bullet(F)$ of a spherical functor $F$ and equip it with a natural paracyclic structure (``rotational symmetry''). This fulfills a part of the general program to provide a rigorous account of perverse schobers which are (thus far conjectural) categorifications of perverse sheaves. Namely, in terms of our previous identification of perverse sheaves on Riemann surfaces with Milnor sheaves, the relative …
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。