On Chow rings of quiver moduli

Pieter Belmans; Hans Franzen

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arXiv · 2307.01711

On Chow rings of quiver moduli

Pieter Belmans·Hans Franzen

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Abstract

We describe the point class and Todd class in the Chow ring of a quiver moduli space, building on a result of Ellingsrud-Str{\o}mme. This, together with the presentation of the Chow ring by the second author, makes it possible to compute integrals on quiver moduli. To do so we construct a canonical morphism of universal representations in great generality, and along the way point out its relation to the Kodaira-Spencer morphism. We illustrate the results by computing some invariants of some "small" Kronecker moduli spaces. We also prove that the first non-trivial (6-dimensional) Kronecker quiver moduli space is isomorphic to the zero locus of a general section of $\mathcal{Q}^\vee(1)$ on $\operatorname{Gr}(2,8)$.

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Pieter Belmans, Hans Franzen. 2023-07-04. On Chow rings of quiver moduli. https://arxiv.org/abs/2307.01711

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