Quiver $D$-Modules and Homology of Local Systems over an Arrangement of Hyperplanes
| dc.creator | Khoroshkin, S. | |
| dc.creator | Varchenko, A. | |
| dc.date | 2005-10-21 | |
| dc.date | 2006-12-18 | |
| dc.date.accessioned | 2026-07-07T07:35:39Z | |
| dc.date.available | 2026-07-07T07:35:39Z | |
| dc.description | Let $C$ be an arrangement of affine hyperplanes in a complex affine space $X$, $D$ the ring of algebraic differential operators on $X$. We define a category of quivers associated with $C$. A quiver is a collection of vector spaces, attached to strata of the arrangement, and suitable linear maps between the vector spaces . To a quiver we assign a $D$-module on $X$, called the quiver $D$-module. We describe basic operations for $D$-modules in terms of linear algebra of quivers. We give an explicit construction of a free resolution of a quive $D$-module and use the construction to describe the associated perverse sheaf. As an application, we calculate the cohomology of $X$ with coefficients in the quiver perverse sheaf (under certain assumptions). | |
| dc.description | Revised version, 92 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510451 | |
| dc.identifier | http://arxiv.org/abs/math/0510451 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120163 | |
| dc.subject | Quantum Algebra | |
| dc.title | Quiver $D$-Modules and Homology of Local Systems over an Arrangement of Hyperplanes | |
| dc.type | text |