PreprintCC BY 4.0arXiv
Degrees of Fano Quiver Moduli
Abstract
This paper provides methods to compute degrees of Fano quiver moduli and gives explicit degree formulas for two classes of them. One such class is a series of toric Fano varieties that parametrize isomorphism classes of representations of the bipartite quiver K(2,q)m with dimension vector underline1, and the other class is the moduli space of q-point configurations on ℙ1. In the former case, we obtain a formula comprised of sums of binomial coefficients in q and m. Its special case m = 1 turns out to be the same as the central MacMahon numbers (OEIS entry A177043). In the latter case, we obtained a formula over ℚ. These formulas are much more efficient than computing directly in Chow rings.
Related
- Series of Fano quiver moduli from extended Dynkin quivers
- Ample stability implies rigidity for quiver moduli
- Degenerations of elliptic quartics and K-moduli of Fano threefolds
- Quantum error correcting codes from quiver moduli: Grassmannians, cyclic monodromy, and argyle collision divisors
- Reflection functors for non-simply-laced quiver varieties
BibTeX
@misc{zhang2026degrees,
title = {{Degrees of Fano Quiver Moduli}},
author = {Pengcheng Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13599},
eprint = {2609.13599},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13599},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Degrees of Fano Quiver Moduli
AU - Pengcheng Zhang
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13599
UR - https://arxiv.org/abs/2609.13599
AB - This paper provides methods to compute degrees of Fano quiver moduli and gives explicit degree formulas for two classes of them. One such class is a series of toric Fano varieties that parametrize isomorphism classes of representations of the bipartite quiver K_(2,q)^m with dimension vector underline1, and the other class is the moduli space of q-point configurations on ℙ^1. In the former case, we obtain a formula comprised of sums of binomial coefficients in q and m. Its special case m = 1 turns out to be the same as the central MacMahon numbers (OEIS entry A177043). In the latter case, we obtained a formula over ℚ. These formulas are much more efficient than computing directly in Chow rings.
ER -