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arXiv · 2609.13599

Degrees of Fano Quiver Moduli

Pengcheng Zhang
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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 $\underline{1}$, and the other class is the moduli space of q-point configurations on $\mathbb{P}^1$. 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 $\mathbb{Q}$. These formulas are much more efficient than computing directly in Chow rings.

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BibTeXRIS

Pengcheng Zhang. 2026-09-11. Degrees of Fano Quiver Moduli. https://arxiv.org/abs/2609.13599

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