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arXiv · 1909.01030

Motive of the moduli stack of rational curves on a weighted projective stack

Jun-Yong Park·Hunter Spink
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Abstract

We show the compactly supported motive of the moduli stack of degree $n$ rational curves on the weighted projective stack $\mathcal{P}(a,b)$ is of mixed Tate type over any base field $K$ with $\text{char}(K) \nmid a,b$ and has class $\mathbb{L}^{(a+b)n+1}-\mathbb{L}^{(a+b)n-1}$ in the Grothendieck ring of stacks. In particular, this improves upon the result of [HP] regarding the arithmetic invariant of the moduli stack $\mathcal{L}_{1,12n} := \mathrm{Hom}_{n}(\mathbb{P}^1, \overline{\mathcal{M}}_{1,1})$ of stable elliptic fibrations over $\mathbb{P}^{1}$ with $12n$ nodal singular fibers and a marked Weierstrass section.

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Jun-Yong Park, Hunter Spink. 2019-09-03. Motive of the moduli stack of rational curves on a weighted projective stack. https://doi.org/10.1007/s40687-020-00236-1

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