{"title":"Multiplicites and modifications, and singularities associated to blowing down negative vector bundles","authors":"Fusheng Deng, Yinji Li, Qunhuan Liu, Xiangyu Zhou","doi":"arxiv-2409.09407","DOIUrl":null,"url":null,"abstract":"We first present the mixed Hilbert-Samuel multiplicities of analytic local\nrings over \\mathbb{C} as generalized Lelong numbers and further represent them\nas intersection numbers in the context of modifications. As applications, we\ngive estimates or an exact formula for the multiplicities of isolated\nsingularities that given by the Grauert blow-downs of negative holomorphic\nvector bundles.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"50 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09407","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We first present the mixed Hilbert-Samuel multiplicities of analytic local
rings over \mathbb{C} as generalized Lelong numbers and further represent them
as intersection numbers in the context of modifications. As applications, we
give estimates or an exact formula for the multiplicities of isolated
singularities that given by the Grauert blow-downs of negative holomorphic
vector bundles.