Relations on \overline{ℳ}_{ℊ,𝓃} via orbifold stable maps

Clader, Emily

doi:10.1090/proc/13344

Relations on $\overline {\mathcal {M}}_{g,n}$ via orbifold stable maps
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by Emily Clader

Proc. Amer. Math. Soc. 145 (2017), 11-21

DOI: https://doi.org/10.1090/proc/13344

Published electronically: September 15, 2016

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Abstract:

Using the equivariant virtual cycle of the moduli space of stable maps to $[\mathbb {C}/\mathbb {Z}_r]$, or equivalently, the vanishing of high-degree Chern classes of a certain vector bundle over the moduli space of stable maps to $B\mathbb {Z}_r$, we derive relations in the Chow ring of $\overline {\mathcal {M}}_{g,n}(B\mathbb {Z}_r,0)$. These push forward to yield tautological relations on $\overline {\mathcal {M}} _{g,n}$.

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