{"title":"特征2中$\\mathbf{A}^{4}/A_{4}$的渐进解析","authors":"Linghu Fan","doi":"10.3792/pjaa.99.014","DOIUrl":null,"url":null,"abstract":"In this paper, we construct a crepant resolution for the quotient singularity $\\mathbf{A}^{4}/A_{4}$ in characteristic 2, where $A_{4}$ is the alternating group of degree 4 with permutation action on $\\mathbf{A}^{4}$. By computing the Euler number of the crepant resolution, we obtain a new counterexample to an analogous statement of McKay correspondence in positive characteristic.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Crepant resolution of $\\\\mathbf{A}^{4}/A_{4}$ in characteristic 2\",\"authors\":\"Linghu Fan\",\"doi\":\"10.3792/pjaa.99.014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we construct a crepant resolution for the quotient singularity $\\\\mathbf{A}^{4}/A_{4}$ in characteristic 2, where $A_{4}$ is the alternating group of degree 4 with permutation action on $\\\\mathbf{A}^{4}$. By computing the Euler number of the crepant resolution, we obtain a new counterexample to an analogous statement of McKay correspondence in positive characteristic.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3792/pjaa.99.014\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3792/pjaa.99.014","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Crepant resolution of $\mathbf{A}^{4}/A_{4}$ in characteristic 2
In this paper, we construct a crepant resolution for the quotient singularity $\mathbf{A}^{4}/A_{4}$ in characteristic 2, where $A_{4}$ is the alternating group of degree 4 with permutation action on $\mathbf{A}^{4}$. By computing the Euler number of the crepant resolution, we obtain a new counterexample to an analogous statement of McKay correspondence in positive characteristic.
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