Flag Varieties of General Quiver Representations: Characteristic Classes and Semi-Invariants
Year: 2026
Type: preprint
Abstract: We study flags of subrepresentations of a general representation of a finite quiver. For each representation, its flag scheme is the zero scheme of a section of a quotient bundle on a product of partial flag varieties. We obtain the generic dimension and cycle class and equivariant localization formulas for Euler characteristics and parabolic Schubert coefficients. We further express these coefficients as finite signed sums of semi-invariant dimensions for auxiliary star quivers with inward and outward flag arms. In the acyclic one-step case, this is compatible with the result of Derksen--Schofield--Weyman, and the zero-dimensional case recovers their semi-invariant counting theorem. Examples treat matrix pencils and generalized Kronecker quivers.
Source: arXiv (Cornell University)
Author: Fei, Jiarui
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4656525603
OpenAlex ID: W7168350090