Perverse sheaves, Koszul IC-modules, and the quiver for the category O

Maxim Vybornov

Home/Archive/arXiv

arXiv · math/0309247

Perverse sheaves, Koszul IC-modules, and the quiver for the category O

Maxim Vybornov

View original source ↗Read source document ↗Export metadata ↓

Abstract

For a stratified topological space we introduce the category of IC-modules, which are linear algebra devices with the relations described by the equation d^2=0. We prove that the category of (mixed) IC-modules is equivalent to the category of (mixed) perverse sheaves for flag varieties. As an application, we describe an algorithm calculating the quiver underlying the BGG category O for arbitrary simple Lie algebra, thus answering a question which goes back to I. M. Gelfand.

Explore related subjects

math.AG math.AT math.RT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Maxim Vybornov. 2006-06-03. Perverse sheaves, Koszul IC-modules, and the quiver for the category O. https://arxiv.org/abs/math/0309247

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

K-stable Fano 3-folds in the families 2.18 and 3.4

We prove that smooth Fano 3-folds in the families 2.18 and 3.4 are K-stable.

math.AG↗

arXiv2026

G3-Criteria and Applications

The G3-property of a subvariety was introduced by Hironaka-Matsumura, and plays an important role for deducing connectedness and extension results. Unfortunately, it's a rather elusive notion, which is not always easy to establish. Most of the existing work is concentrated on subvarieties of homogeneous varieties. The first goal of this article is to show that mobility assumptions on the subvariety, considered in works of Badescu, Chow, Debarre, Voisin, yield a certain partial positivity property, slightly stronger than G3, previously introduced by the author. Second, we apply the result to prove that, in numerous situations, the splitting of the normal bundle of a smooth two-codimensional subvariety implies that it is a complete intersection.

math.AG↗

arXiv2026

Nodal degeneration of chiral algebras I: Global structure and gluing formula

We define a natural extension of a universal factorization algebra $\mathcal{A}$ to families of stable punctured curves, by integrating over all semistable modifications. We prove that the resulting sheaf of factorization homology satisfies a natural gluing formula, by tensoring over a certain derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$, generalizing the Verlinde formula for gluing of conformal blocks.

math.AG↗