Flag Varieties of General Quiver Representations: Characteristic Classes and Semi-Invariants
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.
Related
- Grothendieck ring of varieties and at-the-characteristic numerical invariants
- Triviality of K-homology classes of Euler characteristic operators of stratified pseudomanifolds
- Recovering curves from isogeny classes of Prym varieties
- Independence of the Grothendieck classes of twisted symplectic flag varieties
- Invariants of big classes from asymptotic total Betti numbers
BibTeX
@misc{fei2026flag,
title = {{Flag Varieties of General Quiver Representations: Characteristic Classes and Semi-Invariants}},
author = {Jiarui Fei},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.12458},
eprint = {2607.12458},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.12458},
}
RIS
TY - UNPB
TI - Flag Varieties of General Quiver Representations: Characteristic Classes and Semi-Invariants
AU - Jiarui Fei
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2607.12458
UR - https://arxiv.org/abs/2607.12458
AB - 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.
ER -