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A Topological Characterization of the Middle Perversity Intersection Complex for Arbitrary Complex Algebraic Varieties 任意复数代数变种的中反常交复的拓扑刻画
IF 0.4
Journal of Singularities Pub Date : 2019-05-29 DOI: 10.5427/jsing.2020.20c
Ben Wu
{"title":"A Topological Characterization of the Middle Perversity Intersection Complex for Arbitrary Complex Algebraic Varieties","authors":"Ben Wu","doi":"10.5427/jsing.2020.20c","DOIUrl":"https://doi.org/10.5427/jsing.2020.20c","url":null,"abstract":"For an arbitrary complex algebraic variety which is not necessarily pure dimensional, the intersection complex can be defined as the direct sum of the Deligne-Goresky-Macpherson intersection complexes of each irreducible component. We give two axiomatic topological characterizations of the middle perversity direct sum intersection complex, one stratification dependent and the other stratification independent. To accomplish this, we show that this direct sum intersection complex can be constructed using Deligne's construction in the more general context of topologically stratified spaces. A consequence of these characterizations is the invariance of this direct sum intersection complex under homeomorphisms.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88349313","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}
引用次数: 4
Irreducible holonomy groups and Riccati foliations in higher complex dimension 高复维不可约完整群与Riccati叶
IF 0.4
Journal of Singularities Pub Date : 2019-04-16 DOI: 10.5427/jsing.2019.19j
V. Le'on, M. Martelo, B. Sc'ardua
{"title":"Irreducible holonomy groups and Riccati foliations in higher complex dimension","authors":"V. Le'on, M. Martelo, B. Sc'ardua","doi":"10.5427/jsing.2019.19j","DOIUrl":"https://doi.org/10.5427/jsing.2019.19j","url":null,"abstract":"We study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by a similar property of the fundamental group of the complement of an irreducible hypersurface in the complex projective space. Natural examples of such groups of germ maps are given by holonomy groups and monodromy groups of integrable systems (foliations) under certain conditions on the singular or ramification set. The case of complex dimension one is studied in [7] where finiteness is proved for irreducible groups under certain arithmetic hypothesis on the linear part. In dimension $n geq 2$ the picture changes since linear groups are not always abelian in dimension two or bigger. Nevertheless, we still obtain a finiteness result under some conditions in the linear part of the group, for instance if the linear part is abelian. Examples are given illustrating the role of our hypotheses. Applications are given to the framework of holomorphic foliations and analytic deformations of rational fibrations by Riccati foliations.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76343230","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}
引用次数: 0
Two short proofs of the topological invariance of intersection homology 交同调拓扑不变性的两个简短证明
IF 0.4
Journal of Singularities Pub Date : 2019-04-13 DOI: 10.5427/jsing.2022.25h
Greg Friedman
{"title":"Two short proofs of the topological invariance of intersection homology","authors":"Greg Friedman","doi":"10.5427/jsing.2022.25h","DOIUrl":"https://doi.org/10.5427/jsing.2022.25h","url":null,"abstract":"We indicate two short proofs of the Goresky-MacPherson topological invariance of intersection homology. One proof is very short but requires the Goresky-MacPherson support and cosupport axioms; the other is slightly longer but does not require these axioms and so is adaptable to more general perversities.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88268290","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}
引用次数: 2
Multiplicative de Rham Theorems for Relative and Intersection Space Cohomology 相对和相交空间上同调的乘法de Rham定理
IF 0.4
Journal of Singularities Pub Date : 2019-03-31 DOI: 10.5427/jsing.2019.19g
F. Schloder, J. Essig
{"title":"Multiplicative de Rham Theorems for Relative and Intersection Space Cohomology","authors":"F. Schloder, J. Essig","doi":"10.5427/jsing.2019.19g","DOIUrl":"https://doi.org/10.5427/jsing.2019.19g","url":null,"abstract":"We construct an explicit de Rham isomorphism relating the cohomology rings of Banagl's de Rham and spatial approach to intersection space cohomology for stratified pseudomanifolds with isolated singularities. Intersection space (co-)homology is a modified (co-)homology theory extending Poincare Duality to stratified pseudomanifolds. The novelty of our result compared to the de Rham isomorphism given previously by Banagl is, that we indeed have an isomorphism of rings and not just of graded vector spaces. We also provide a proof of the de Rham Theorem for cohomology rings of pairs of smooth manifolds which we use in the proof of our main result.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77793005","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}
引用次数: 3
Real and complex integral closure, Lipschitz equisingularity and applications on square matrices 实和复积分闭包，Lipschitz等奇异性及其在方阵上的应用
IF 0.4
Journal of Singularities Pub Date : 2019-02-28 DOI: 10.5427/jsing.2020.22o
T. F. Silva, N. Grulha, M. S. Pereira
{"title":"Real and complex integral closure, Lipschitz equisingularity and applications on square matrices","authors":"T. F. Silva, N. Grulha, M. S. Pereira","doi":"10.5427/jsing.2020.22o","DOIUrl":"https://doi.org/10.5427/jsing.2020.22o","url":null,"abstract":"Recently the authors investigated the Lipschitz triviality of simple germs of matrices. In this work, we improve some previous results and we present an extension of an integral closure result for the real setting. These tools are applied to investigate classes of square matrices singularities classified by Bruce and Tari.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74133589","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}
引用次数: 0
Chaos in periodically forced reversible vector fields 周期强迫可逆向量场中的混沌
IF 0.4
Journal of Singularities Pub Date : 2019-01-25 DOI: 10.5427/jsing.2020.22p
I. Labouriau, Elisa Sovrano
{"title":"Chaos in periodically forced reversible vector fields","authors":"I. Labouriau, Elisa Sovrano","doi":"10.5427/jsing.2020.22p","DOIUrl":"https://doi.org/10.5427/jsing.2020.22p","url":null,"abstract":"We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of pulse form may be added to them to yield topological chaotic behaviour. Chaos here means that the resulting dynamics is semi-conjugate to a shift in a finite alphabet. \u0000The results rely on the classification of reversible vector fields and on the theory of topological horseshoes. This work is part of a project of studying periodic forcing of symmetric vector fields.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77497288","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}
引用次数: 2
On the topology of non-isolated real singularities 关于非孤立实奇点的拓扑
IF 0.4
Journal of Singularities Pub Date : 2019-01-18 DOI: 10.5427/jsing.2020.22j
N. Dutertre
{"title":"On the topology of non-isolated real singularities","authors":"N. Dutertre","doi":"10.5427/jsing.2020.22j","DOIUrl":"https://doi.org/10.5427/jsing.2020.22j","url":null,"abstract":"Khimshiashvili proved a topological degree formula for the Eu-ler characteristic of the Milnor fibres of a real function-germ with an isolated singularity. We give two generalizations of this result for non-isolated singularities. As corollaries we obtain an algebraic formula for the Euler characteristic of the fibres of a real weighted-homogeneous polynomial and a real version of the L{^e}-Iomdine formula. We have also included some results of the same flavor on the local topology of locally closed definable sets.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85962638","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}
引用次数: 5
(Co)torsion of exterior powers of differentials over complete intersections (Co)完全交点上微分的外幂的扭转
IF 0.4
Journal of Singularities Pub Date : 2019-01-01 DOI: 10.5427/jsing.2019.19h
C. Miller, S. Vassiliadou
{"title":"(Co)torsion of exterior powers of differentials over complete intersections","authors":"C. Miller, S. Vassiliadou","doi":"10.5427/jsing.2019.19h","DOIUrl":"https://doi.org/10.5427/jsing.2019.19h","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76350983","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}
引用次数: 2
On Realizations of Some Plane Algebroid Curves 若干平面代数曲线的实现
IF 0.4
Journal of Singularities Pub Date : 2019-01-01 DOI: 10.5427/jsing.2019.19a
A. Bueno, Gheyza Ferreira, Renato Vidal Martins
{"title":"On Realizations of Some Plane Algebroid Curves","authors":"A. Bueno, Gheyza Ferreira, Renato Vidal Martins","doi":"10.5427/jsing.2019.19a","DOIUrl":"https://doi.org/10.5427/jsing.2019.19a","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80261081","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}
引用次数: 0
How to glue parity sheaves 如何粘奇偶轴
IF 0.4
Journal of Singularities Pub Date : 2018-12-19 DOI: 10.5427/jsing.2020.20g
Pramod N. Achar
{"title":"How to glue parity sheaves","authors":"Pramod N. Achar","doi":"10.5427/jsing.2020.20g","DOIUrl":"https://doi.org/10.5427/jsing.2020.20g","url":null,"abstract":"Let X be a stratified space on which the Juteau-Mautner-Williamson theory of parity sheaves is available. We develop a \"nearby cycles formalism\" in the framework of the homotopy category of parity sheaves on X, also known as the mixed modular derived category of X. This construction is expected to have applications in modular geometric representation theory.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84410210","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}
引用次数: 1
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