2021/06/22 by Takahiro Yamamoto, Yamamoto, Takahiro
Mathematics · Physics and Astronomy · #14E15 #14E16 #14L30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:14E15 #msc:14E16 #msc:14L30
paper · pdf · doi:10.48550/arxiv.2106.11526
27 pages, 2 figures
arxiv created 2021/06/22 · openalex publication_date 2021/06/22 · arxiv updated 2021/06/23 · openalex created_date 2021/07/05 · openalex updated_date 2026/07/28
In characteristic zero, if a quotient variety has a crepant resolution, the Euler characteristic of the crepant resolution is equal to the number of conjugacy classes of the acting group, by Batyrev's theorem. This is one of the McKay correspondence. It is natural to consider the analogue statement in the positive characteristic. In this paper, we present sequences of crepant resolutions of quotient varieties in the positive characteristic and show that one of the sequences gives a counterexample to the analogue statement of Batyrev's theorem.