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


Author: Emily Clader
Journal: Proc. Amer. Math. Soc. 145 (2017), 11-21
MSC (2010): Primary 14H10
DOI: https://doi.org/10.1090/proc/13344
Published electronically: September 15, 2016
MathSciNet review: 3565356
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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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Additional Information

Emily Clader
Affiliation: Department of Mathematics, San Francisco State University, Thornton Hall 937, 1600 Holloway Avenue, San Francisco, CA 94132
Email: eclader@sfsu.edu

DOI: https://doi.org/10.1090/proc/13344
Received by editor(s): March 2, 2016
Published electronically: September 15, 2016
Additional Notes: This work was partially supported by FRG grant DMS-1159265, RTG grant DMS-1045119, Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.
Communicated by: Lev Borisov
Article copyright: © Copyright 2016 American Mathematical Society