On convergence of stringy motives of wild pⁿ-cyclic quotient singularities

Abstract

The wild McKay correspondence, a variant of the McKay correspondence in positive characteristics, shows that stringy motives of quotient varieties equal some motivic integrals on the moduli space of the Galois covers of a formal disk. In this paper, we determine when the integral converges for the case of cyclic groups of prime power order. As an application, we give a criterion for the quotient variety being canonical or log canonical.

Keywords:

• Algebraic geometry
• motivic integration
• quotient singularities
• the McKay correspondence

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 14E16
• Secondary: 11S15
• 14B05
• 14E18
• 14G17
• 14R20

Acknowledgments

We would like to thank Takehiko Yasuda and Takahiro Yamamoto for their helpful comments.

Additional information

Funding

This work was supported by JSPS KAKENHI JP18H01112 and JP18K18710.