{"title":"Round fold maps of n-dimensional manifolds into (n-1)-dimensional Euclidean space","authors":"Naoki Kitazawa, O. Saeki","doi":"10.5427/jsing.2023.26a","DOIUrl":"https://doi.org/10.5427/jsing.2023.26a","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"166 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73283053","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}
Our aim is to precisely present a tame topology counterpart to canonical stratification of a Lie groupoid. We consider a definable Lie groupoid in semialgebraic, subanalytic, o-minimal over R, or more generally, Shiota's X-category. We show that there exists a canonical Whitney stratification of the Lie groupoid into definable strata which are invariant under the groupoid action. This is a generalization and refinement of results on real algebraic group action which J.N. Mather and V.A. Vassiliev independently stated with sketchy proofs. A crucial change to their proofs is to use Shiota's isotopy lemma and approximation theorem in the context of tame topology.
{"title":"Canonical stratification of definable Lie groupoids","authors":"Masato Tanabe","doi":"10.5427/jsing.2023.26d","DOIUrl":"https://doi.org/10.5427/jsing.2023.26d","url":null,"abstract":"Our aim is to precisely present a tame topology counterpart to canonical stratification of a Lie groupoid. We consider a definable Lie groupoid in semialgebraic, subanalytic, o-minimal over R, or more generally, Shiota's X-category. We show that there exists a canonical Whitney stratification of the Lie groupoid into definable strata which are invariant under the groupoid action. This is a generalization and refinement of results on real algebraic group action which J.N. Mather and V.A. Vassiliev independently stated with sketchy proofs. A crucial change to their proofs is to use Shiota's isotopy lemma and approximation theorem in the context of tame topology.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135650631","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 investigate Zariski multiples of plane curves Z 1 ,...,Z N such that each Z i is a union of a smooth quartic curve, some of its bitangents, and some of its 4-tangent conics. We show that, for plane curves of this type, the deformation types are equal to the homeomorphism types, and that the number of deformation types grows as O ( d 62 ) when the degree d of the plane curves tends to infinity.
{"title":"Zariski multiples associated with quartic curves","authors":"I. Shimada","doi":"10.5427/jsing.2022.24g","DOIUrl":"https://doi.org/10.5427/jsing.2022.24g","url":null,"abstract":". We investigate Zariski multiples of plane curves Z 1 ,...,Z N such that each Z i is a union of a smooth quartic curve, some of its bitangents, and some of its 4-tangent conics. We show that, for plane curves of this type, the deformation types are equal to the homeomorphism types, and that the number of deformation types grows as O ( d 62 ) when the degree d of the plane curves tends to infinity.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"71 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76778602","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 classify singularities at infinity of polynomials of degree 3 in 3 variables, f(x0, x1, x2) = f1(x0, x1, x2) + f2(x0, x1, x2) + f3(x0, x1, x2), fi homogeneous polynomial of degree i, i = 1, 2, 3. Based on this classification, we calculate the jump in the Milnor number of an isolated singularity at infinity, when we pass from the special fiber to a generic fiber. As an application of the results, we investigate the existence of global fibrations of degree 3 polynomials in C and search for information about the topology of the fibers in each equivalence class.
{"title":"Classification at infinity of polynomials of degree 3 in 3 variables","authors":"N. Ribeiro","doi":"10.5427/jsing.2022.25r","DOIUrl":"https://doi.org/10.5427/jsing.2022.25r","url":null,"abstract":"We classify singularities at infinity of polynomials of degree 3 in 3 variables, f(x0, x1, x2) = f1(x0, x1, x2) + f2(x0, x1, x2) + f3(x0, x1, x2), fi homogeneous polynomial of degree i, i = 1, 2, 3. Based on this classification, we calculate the jump in the Milnor number of an isolated singularity at infinity, when we pass from the special fiber to a generic fiber. As an application of the results, we investigate the existence of global fibrations of degree 3 polynomials in C and search for information about the topology of the fibers in each equivalence class.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"13 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84499867","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":"The Delta Invariant and Fiberwise Normalization for Families of isolated Non-Normal Singularities","authors":"G. Greuel, G. Pfister","doi":"10.5427/jsing.2022.25j","DOIUrl":"https://doi.org/10.5427/jsing.2022.25j","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"21 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78892060","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":"Right Network-Preserving Diffeomorphisms","authors":"F. Antoneli, Ian M. Stewart","doi":"10.5427/jsing.2022.25a","DOIUrl":"https://doi.org/10.5427/jsing.2022.25a","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"3 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81929627","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":"Critical principal singularities of hypersurfaces in Euclidean 4-spaces","authors":"R. Garcia, D. Lopes, J. Sotomayor","doi":"10.5427/jsing.2022.25i","DOIUrl":"https://doi.org/10.5427/jsing.2022.25i","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"15 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82163640","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":"Fundamental group of rational homology disk smoothings of surface singularities","authors":"E. Artal Bartolo, J. Wahl","doi":"10.5427/jsing.2022.24e","DOIUrl":"https://doi.org/10.5427/jsing.2022.24e","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"94 15","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72370978","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":"Homologically trivial integrable deformations of germs of holomorphic functions","authors":"V. León, B. Scárdua","doi":"10.5427/jsing.2022.24d","DOIUrl":"https://doi.org/10.5427/jsing.2022.24d","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"70 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84124479","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":"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":"50 1","pages":""},"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}
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