Rational singularities for moment maps of totally negative quivers
Vernet T. 2024. Rational singularities for moment maps of totally negative quivers. Transformation Groups.
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Abstract
We prove that the zero-fiber of the moment map of a totally negative quiver has rational singularities. Our proof consists in generalizing dimension bounds on jet spaces of this fiber, which were introduced by Budur. We also transfer the rational singularities property to other moduli spaces of objects in 2-Calabi-Yau categories, based on recent work of Davison. This has interesting arithmetic applications on quiver moment maps and moduli spaces of objects in 2-Calabi-Yau categories. First, we generalize results of Wyss on the asymptotic behaviour of counts of jets of quiver moment maps over finite fields. Moreover, we interpret the limit of counts of jets on a given moduli space as its p-adic volume under a canonical measure analogous to the measure built by Carocci, Orecchia and Wyss on certain moduli spaces of coherent sheaves.
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2024-09-09
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Transformation Groups
Acknowledgement
I would like to warmly thank Dimitri Wyss for his guidance and supervision and Nero Budur for helpful discussions and answering all my questions on his previous works. I would also like to thank Francesca Carocci, Ben Davison, Lucien Hennecart and Olivier Schiffmann for helpful remarks and discussions during the writing of this paper. Finally, I would like to thank the anonymous referees for their careful reading and suggesting improvements in the exposition.
Open access funding provided by Institute of Science and Technology (IST Austria). This work was supported by the Swiss National Science Foundation [No. 196960]. This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.
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Cite this
Vernet T. Rational singularities for moment maps of totally negative quivers. Transformation Groups. 2024. doi:10.1007/s00031-024-09873-0
Vernet, T. (2024). Rational singularities for moment maps of totally negative quivers. Transformation Groups. Springer Nature. https://doi.org/10.1007/s00031-024-09873-0
Vernet, Tanguy. “Rational Singularities for Moment Maps of Totally Negative Quivers.” Transformation Groups. Springer Nature, 2024. https://doi.org/10.1007/s00031-024-09873-0.
T. Vernet, “Rational singularities for moment maps of totally negative quivers,” Transformation Groups. Springer Nature, 2024.
Vernet T. 2024. Rational singularities for moment maps of totally negative quivers. Transformation Groups.
Vernet, Tanguy. “Rational Singularities for Moment Maps of Totally Negative Quivers.” Transformation Groups, Springer Nature, 2024, doi:10.1007/s00031-024-09873-0.
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