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arXiv · 2607.12458

Euler Characteristics of Generic Quiver Grassmannians: Semi-Invariants and Localization

Jiarui Fei
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Abstract

We study the topological Euler characteristic of the quiver Grassmannian for a generic representation. We give a Chern class formula and a finite torus-localization formula. If the quiver $Q$ is acyclic, the formula can be combined with the covariant calculation of Derksen--Schofield--Weyman to obtain a finite integral linear combination of covariant multiplicities, or equivalently of semi-invariant multiplicities for a single flag-extended quiver of $Q$. We also give explicit formulas and examples for generalized Kronecker quivers, and record the same construction for multiplicative characteristic genera.

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Jiarui Fei. 2026-07-14. Euler Characteristics of Generic Quiver Grassmannians: Semi-Invariants and Localization. https://arxiv.org/abs/2607.12458

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