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A Fine Property of Sets at Points of Lebesgue Density Lebesgue密度点上集合的一个优良性质
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-01-01 DOI: 10.1307/mmj/20205874
S. Delladio
{"title":"A Fine Property of Sets at Points of Lebesgue Density","authors":"S. Delladio","doi":"10.1307/mmj/20205874","DOIUrl":"https://doi.org/10.1307/mmj/20205874","url":null,"abstract":"","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72807455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Effect of Cell-Attachment on the Group of Self-Equivalences of an Elliptic Space 椭圆空间自等价群上的细胞附著效应
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-01-01 DOI: 10.1307/MMJ/20195840
M. Benkhalifa
{"title":"The Effect of Cell-Attachment on the Group of Self-Equivalences of an Elliptic Space","authors":"M. Benkhalifa","doi":"10.1307/MMJ/20195840","DOIUrl":"https://doi.org/10.1307/MMJ/20195840","url":null,"abstract":"","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79518228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
A Valuation Theorem for Noetherian Rings noether环的一个值定理
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2020-11-30 DOI: 10.1307/mmj/20206022
Antoni Rangachev
{"title":"A Valuation Theorem for Noetherian Rings","authors":"Antoni Rangachev","doi":"10.1307/mmj/20206022","DOIUrl":"https://doi.org/10.1307/mmj/20206022","url":null,"abstract":"Let A and B be integral domains. Suppose A is Noetherian and B is a finitely generated A-algebra that contains A. Denote by A' the integral closure of A in B. We show that A' is determined by finitely many unique discrete valuation rings. Our result generalizes Rees' classical valuation theorem for ideals. We also obtain a variant of Zariski's main theorem.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76208951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Length of PU(2,1) Relative to Special Elliptic Isometries with Fixed Parameter PU(2,1)相对于固定参数特殊椭圆等距的长度
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2020-10-28 DOI: 10.1307/mmj/20206013
Felipe de Aguilar Franco
{"title":"The Length of PU(2,1) Relative to Special Elliptic Isometries with Fixed Parameter","authors":"Felipe de Aguilar Franco","doi":"10.1307/mmj/20206013","DOIUrl":"https://doi.org/10.1307/mmj/20206013","url":null,"abstract":"Generalizing the involution length of the complex hyperbolic plane, we obtain that the α -length of PU(2 , 1) is 4, that is, every element of PU(2 , 1) can be decomposed as the product of at most 4 special elliptic isometries with parameter α . We also describe the isometries that can be written as the product of 2 or 3 such special elliptic isometries.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74598415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Unexpected Properties of the Klein Configuration of 60 Points in P3 P3中60点Klein组态的意外性质
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2020-10-17 DOI: 10.1307/mmj/20216141
Piotr Pokora, T. Szemberg, J. Szpond
{"title":"Unexpected Properties of the Klein Configuration of 60 Points in P3","authors":"Piotr Pokora, T. Szemberg, J. Szpond","doi":"10.1307/mmj/20216141","DOIUrl":"https://doi.org/10.1307/mmj/20216141","url":null,"abstract":"Felix Klein in course of his study of the regular icosahedron and its symmetries encountered a highly symmetric configuration of $60$ points in ${mathbb P}^3$. This configuration has appeared in various guises, perhaps post notably as the configuration of points dual to the $60$ reflection planes in the group $G_{31}$ in the Shephard-Todd list. In the present note we show that the $60$ points exhibit interesting properties relevant from the point of view of two paths of research initiated recently. Firstly, they give rise to two completely different unexpected surfaces of degree $6$. Unexpected hypersurfaces have been introduced by Cook II, Harbourne, Migliore, Nagel in 2018. One of unexpected surfaces associated to the configuration of $60$ points is a cone with a single singularity of multiplicity $6$ and the other has three singular points of multiplicities $4,2$ and $2$. Secondly, Chiantini and Migliore observed in 2020 that there are non-trivial sets of points in ${mathbb P}^3$ with the surprising property that their general projection to ${mathbb P}^2$ is a complete intersection. They found a family of such sets, which they called grids. An appendix to their paper describes an exotic configuration of $24$ points in ${mathbb P}^3$ which is not a grid but has the remarkable property that its general projection is a complete intersection. We show that the Klein configuration is also not a grid and it projects to a complete intersections. We identify also its proper subsets, which enjoy the same property. ","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85250072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Connectedness Principle for 3-Folds in Characteristic p>5 特征p>5的3-褶皱连通性原理
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2020-10-16 DOI: 10.1307/mmj/20216143
Stefano Filipazzi, J. Waldron
{"title":"Connectedness Principle for 3-Folds in Characteristic p>5","authors":"Stefano Filipazzi, J. Waldron","doi":"10.1307/mmj/20216143","DOIUrl":"https://doi.org/10.1307/mmj/20216143","url":null,"abstract":"A conjecture, known as the Shokurov-Koll'ar connectedness principle, predicts the following. Let $(X,B)$ be a pair, and let $f colon X rightarrow S$ be a contraction with $-(K_X + B)$ nef over $S$; then, for any point $s in S$, the intersection $f^{-1} (s) cap mathrm{Nklt}(X,B)$ has at most two connected components, where $mathrm{Nklt}(X,B)$ denotes the non-klt locus of $(X,B)$. This conjecture has been extensively studied in characteristic zero, and it has been recently settled in that context. In this work, we consider this conjecture in the setup of positive characteristic algebraic geometry. We prove this conjecture holds for threefolds in characteristic $p>5$, and, under the same assumptions, we characterize the cases in which $mathrm{Nklt}(X,B)$ fails to be connected.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72805598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Trisections of Nonorientable 4-Manifolds 不可定向4-流形的三切分
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2020-10-14 DOI: 10.1307/mmj/20216127
Maggie Miller, Patrick Naylor
{"title":"Trisections of Nonorientable 4-Manifolds","authors":"Maggie Miller, Patrick Naylor","doi":"10.1307/mmj/20216127","DOIUrl":"https://doi.org/10.1307/mmj/20216127","url":null,"abstract":"We study trisections of smooth, compact non-orientable 4-manifolds, and introduce trisections of non-orientable 4-manifolds with boundary. In particular, we prove a non-orientable analogue of a classical theorem of Laudenbach-Poenaru. As a consequence, trisection diagrams and Kirby diagrams of closed non-orientable 4-manifolds exist. We discuss how the theory of trisections may be adapted to the setting of non-orientable 4-manifolds with many examples.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76901734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Index 指数
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2020-10-01 DOI: 10.1307/mmj/1604044881
{"title":"Index","authors":"","doi":"10.1307/mmj/1604044881","DOIUrl":"https://doi.org/10.1307/mmj/1604044881","url":null,"abstract":"","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80512809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonminimal Bridge Position of 2-Cable Links 2-电缆连接的非最小桥架位置
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2020-09-10 DOI: 10.1307/mmj/20216060
Jung Hoon Lee
{"title":"Nonminimal Bridge Position of 2-Cable Links","authors":"Jung Hoon Lee","doi":"10.1307/mmj/20216060","DOIUrl":"https://doi.org/10.1307/mmj/20216060","url":null,"abstract":"Suppose that every non-minimal bridge position of a knot $K$ is perturbed. We show that if $L$ is a $(2, 2q)$-cable link of $K$, then every non-minimal bridge position of $L$ is also perturbed.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90352223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Croke–Kleiner Admissible Groups: Property (QT) and Quasiconvexity Croke-Kleiner可容许群:性质(QT)和拟共凸性
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2020-09-07 DOI: 10.1307/mmj/20216045
H. Nguyen, Wen-yuan Yang
{"title":"Croke–Kleiner Admissible Groups: Property (QT) and Quasiconvexity","authors":"H. Nguyen, Wen-yuan Yang","doi":"10.1307/mmj/20216045","DOIUrl":"https://doi.org/10.1307/mmj/20216045","url":null,"abstract":"Croke-Kleiner admissible groups firstly introduced by Croke-Kleiner belong to a particular class of graph of groups which generalize fundamental groups of $3$--dimensional graph manifolds. In this paper, we show that if $G$ is a Croke-Kleiner admissible group, acting geometrically on a CAT(0) space $X$, then a finitely generated subgroup of $G$ has finite height if and only if it is strongly quasi-convex. We also show that if $G curvearrowright X$ is a flip CKA action then $G$ is quasi-isometric embedded into a finite product of quasi-trees. With further assumption on the vertex groups of the flip CKA action $G curvearrowright X$, we show that $G$ satisfies property (QT) that is introduced by Bestvina-Bromberg-Fujiwara.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73981490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
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