{"title":"Bi-Lipschitz and differentiable sufficiency of weighted jets","authors":"J. Costa, M. Saia, Carlos Humberto Soares Junior","doi":"10.5427/jsing.2022.25f","DOIUrl":"https://doi.org/10.5427/jsing.2022.25f","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76830503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Topological classification of circle-valued simple Morse-Bott functions on closed orientable surfaces","authors":"E. B. Batista, J. Costa, I. S. Meza-Sarmiento","doi":"10.5427/jsing.2018.17q","DOIUrl":"https://doi.org/10.5427/jsing.2018.17q","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79453223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We discuss examples of smooth quasi-projective manifolds with non-reduced Alexander modules, giving a non-semisimple Alexander module in one variable case and prove a result giving sufficient conditions for semisimplicity.
{"title":"Remarks on semi-simplicity of Alexander modules","authors":"A. Libgober","doi":"10.5427/jsing.2022.25n","DOIUrl":"https://doi.org/10.5427/jsing.2022.25n","url":null,"abstract":"We discuss examples of smooth quasi-projective manifolds with non-reduced Alexander modules, giving a non-semisimple Alexander module in one variable case and prove a result giving sufficient conditions for semisimplicity.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88453466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Monster towers from differential and algebraic viewpoints","authors":"P. Mormul","doi":"10.5427/jsing.2022.25o","DOIUrl":"https://doi.org/10.5427/jsing.2022.25o","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88522220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On bi-Lipschitz invariance and the uniqueness of tangent cones","authors":"J. E. Sampaio, E. D. da Silva","doi":"10.5427/jsing.2022.25s","DOIUrl":"https://doi.org/10.5427/jsing.2022.25s","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75418880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Brasselet, Nivaldo G. Grulha Jr., Thuy Thi Bích Nguyên
{"title":"Local Euler obstruction, old and new, III","authors":"J. Brasselet, Nivaldo G. Grulha Jr., Thuy Thi Bích Nguyên","doi":"10.5427/jsing.2022.25e","DOIUrl":"https://doi.org/10.5427/jsing.2022.25e","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80880909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Invariants and classification of simple function germs with respect to Lipschitz A-equivalence","authors":"Nhan Nguyen, S. Trivedi","doi":"10.5427/jsing.2022.25p","DOIUrl":"https://doi.org/10.5427/jsing.2022.25p","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74429213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Raimundo Nonato Araújo dos Santos, O. Saeki, T. O. Souza
{"title":"Algebraic knots associated with Milnor fibrations","authors":"Raimundo Nonato Araújo dos Santos, O. Saeki, T. O. Souza","doi":"10.5427/jsing.2022.25b","DOIUrl":"https://doi.org/10.5427/jsing.2022.25b","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88594503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that the sum of the local cohomological dimension and the rectified $mathbb Q$-homological depth of a closed analytic subspace of a complex manifold coincide with the dimension of the ambient manifold. The local cohomological dimension is then calculated using the cohomology of the links of the analytic space. In the algebraic case the first assertion is equivalent to the coincidence of the rectified $mathbb Q$-homological depth with the de Rham depth studied by Ogus, and follows essentially from his work. As a corollary we show that the local cohomological dimension of a quasi-projective variety is determined by that of its general hyperplane section together with the link cohomology at 0-dimensional strata of a complex analytic Whitney stratification.
{"title":"Topological calculation of local cohomological dimension","authors":"Thomas Reichelt, M. Saito, U. Walther","doi":"10.5427/jsing.2023.26b","DOIUrl":"https://doi.org/10.5427/jsing.2023.26b","url":null,"abstract":"We show that the sum of the local cohomological dimension and the rectified $mathbb Q$-homological depth of a closed analytic subspace of a complex manifold coincide with the dimension of the ambient manifold. The local cohomological dimension is then calculated using the cohomology of the links of the analytic space. In the algebraic case the first assertion is equivalent to the coincidence of the rectified $mathbb Q$-homological depth with the de Rham depth studied by Ogus, and follows essentially from his work. As a corollary we show that the local cohomological dimension of a quasi-projective variety is determined by that of its general hyperplane section together with the link cohomology at 0-dimensional strata of a complex analytic Whitney stratification.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80902712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
From a procedure to calculate the $C_5$-cone of a reduced complex analytic curve $X subset mathbb{C}^n$ at a singular point $0 in X$, we extract a collection of integers that we call {it auxiliary multiplicities} and we prove they characterize the Lipschitz type of complex curve singularities. We then use them to improve the known bounds for the number of irreducible components of the $C_5$-cone. We finish by giving an example showing that in a Lipschitz equisingular family of curves the number of planes in the $C_5$-cone may not be constant.
{"title":"On the fifth Whitney cone of a complex analytic curve","authors":"A. G. Flores, O. N. Silva, J. Snoussi","doi":"10.5427/jsing.2022.24c","DOIUrl":"https://doi.org/10.5427/jsing.2022.24c","url":null,"abstract":"From a procedure to calculate the $C_5$-cone of a reduced complex analytic curve $X subset mathbb{C}^n$ at a singular point $0 in X$, we extract a collection of integers that we call {it auxiliary multiplicities} and we prove they characterize the Lipschitz type of complex curve singularities. We then use them to improve the known bounds for the number of irreducible components of the $C_5$-cone. We finish by giving an example showing that in a Lipschitz equisingular family of curves the number of planes in the $C_5$-cone may not be constant.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75640045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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