# Perverse Schobers

@inproceedings{Kapranov2014PerverseS, title={Perverse Schobers}, author={Mikhail M. Kapranov and Vadim Schechtman}, year={2014} }

The notion of a perverse sheaf, introduced in [BBD], has come to play a central role in algebraic geometry and representation theory. In particular, appropriate categories of perverse sheaves provide “categorifications” of various representation spaces, these spaces being recovered as the Grothedieck groups of the categories. The goal of this paper is to suggest the possibility of categorifying the very concept of a perverse sheaf. In other words, we propose to develop a theory of perverse…

## 34 Citations

### A class of perverse schobers in Geometric Invariant Theory

- Mathematics
- 2019

Perverse schobers are categorifications of perverse sheaves. We construct a perverse schober on a partial compactification of the stringy Kahler moduli space (SKMS) associated by Halpern-Leistner and…

### PERVERSE SHEAVES AND D-MODULES

- Mathematics
- 2019

In recent years, sheaf-theoretic constructions have begun to play an increasingly important role in Floer theory in symplectic topology and gauge theory; in many special cases there now exist…

### Categorification of Legendrian knots

- Mathematics
- 2019

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…

### Perverse schobers on Riemann surfaces: constructions and examples

- MathematicsEuropean Journal of Mathematics
- 2018

This note studies perverse sheaves of categories, or schobers, on Riemann surfaces, following ideas of Kapranov and Schechtman (Perverse schobers, arXiv:1411.2772, 2014). For certain wall crossings…

### New description of perverse sheaves on a disc

- Mathematics
- 2022

There is a connection between the category of perverse sheaves on a disc and different notions related to spherical functors. We introduce a category whose objects are analogous to 4periodic…

### Derived category of projectivizations and flops

- Mathematics
- 2018

We prove a generalization of Orlov’s projectivization formula for the derived category D coh(P(E )), where E does not need to be a vector bundle; Instead, E is a coherent sheaf which locally admits…

### Shuffle algebras and perverse sheaves

- MathematicsPure and Applied Mathematics Quarterly
- 2020

We relate shuffle algebras, as defined by Nichols, Feigin-Odesskii and Rosso, to perverse sheaves on symmetric products of the complex line (i.e., on the spaces of monic polynomials stratified by…

### Cluster theory of topological Fukaya categories

- Mathematics
- 2022

We study a class of generalized cluster categories arising from relative Ginzburg algebras of triangulated marked surfaces without punctures. We show that these categories describe 1periodic versions…

### Calabi-Yau structures, spherical functors, and shifted symplectic structures

- MathematicsAdvances in Mathematics
- 2021

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