Abstract By use of a natural map introduced recently by the first and third authors from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the small differentiable deformation of this manifold, we will give a power series proof for Kodaira–Spencer’s local stability theorem of Kähler structures. We also obtain two new local stability theorems, one of balanced structures on an n-dimensional balanced manifold with the $(n-1,n)$ th mild $partial overline {partial }$ -lemma by power series method and the other one on p-Kähler structures with the deformation invariance of $(p,p)$ -Bott–Chern numbers.
{"title":"POWER SERIES PROOFS FOR LOCAL STABILITIES OF KÄHLER AND BALANCED STRUCTURES WITH MILD \u0000$partial overline {partial }$\u0000 -LEMMA","authors":"S. Rao, Xueyuan Wan, Quanting Zhao","doi":"10.1017/nmj.2021.4","DOIUrl":"https://doi.org/10.1017/nmj.2021.4","url":null,"abstract":"Abstract By use of a natural map introduced recently by the first and third authors from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the small differentiable deformation of this manifold, we will give a power series proof for Kodaira–Spencer’s local stability theorem of Kähler structures. We also obtain two new local stability theorems, one of balanced structures on an n-dimensional balanced manifold with the \u0000$(n-1,n)$\u0000 th mild \u0000$partial overline {partial }$\u0000 -lemma by power series method and the other one on p-Kähler structures with the deformation invariance of \u0000$(p,p)$\u0000 -Bott–Chern numbers.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"246 1","pages":"305 - 354"},"PeriodicalIF":0.8,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nmj.2021.4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48068824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We establish adjunction and inversion of adjunction for log canonical centers of arbitrary codimension in full generality.
摘要本文建立了任意余维对数正则中心的完全一般的附结和附结反演。
{"title":"ADJUNCTION AND INVERSION OF ADJUNCTION","authors":"O. Fujino, K. Hashizume","doi":"10.1017/nmj.2022.24","DOIUrl":"https://doi.org/10.1017/nmj.2022.24","url":null,"abstract":"Abstract We establish adjunction and inversion of adjunction for log canonical centers of arbitrary codimension in full generality.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"249 1","pages":"119 - 147"},"PeriodicalIF":0.8,"publicationDate":"2021-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43057417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Improving and clarifying a construction of Horowitz and Shelah, we show how to construct (in $mathsf {ZF}$ , i.e., without using the Axiom of Choice) maximal cofinitary groups. Among the groups we construct, one is definable by a formula in second-order arithmetic with only a few natural number quantifiers.
{"title":"CONSTRUCTING MAXIMAL COFINITARY GROUPS","authors":"David Schrittesser","doi":"10.1017/nmj.2022.46","DOIUrl":"https://doi.org/10.1017/nmj.2022.46","url":null,"abstract":"Abstract Improving and clarifying a construction of Horowitz and Shelah, we show how to construct (in \u0000$mathsf {ZF}$\u0000 , i.e., without using the Axiom of Choice) maximal cofinitary groups. Among the groups we construct, one is definable by a formula in second-order arithmetic with only a few natural number quantifiers.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"251 1","pages":"622 - 651"},"PeriodicalIF":0.8,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44324189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We study the action of a real reductive group G on a real submanifold X of a Kähler manifold Z. We suppose that the action of a compact connected Lie group U with Lie algebra $mathfrak {u}$ extends holomorphically to an action of the complexified group $U^{mathbb {C}}$ and that the U-action on Z is Hamiltonian. If $Gsubset U^{mathbb {C}}$ is compatible, there exists a gradient map $mu _{mathfrak p}:X longrightarrow mathfrak p$ where $mathfrak g=mathfrak k oplus mathfrak p$ is a Cartan decomposition of $mathfrak g$ . In this paper, we describe compact orbits of parabolic subgroups of G in terms of the gradient map $mu _{mathfrak p}$ .
{"title":"COMPACT ORBITS OF PARABOLIC SUBGROUPS","authors":"L. Biliotti, O. J. Windare","doi":"10.1017/nmj.2021.14","DOIUrl":"https://doi.org/10.1017/nmj.2021.14","url":null,"abstract":"Abstract We study the action of a real reductive group G on a real submanifold X of a Kähler manifold Z. We suppose that the action of a compact connected Lie group U with Lie algebra \u0000$mathfrak {u}$\u0000 extends holomorphically to an action of the complexified group \u0000$U^{mathbb {C}}$\u0000 and that the U-action on Z is Hamiltonian. If \u0000$Gsubset U^{mathbb {C}}$\u0000 is compatible, there exists a gradient map \u0000$mu _{mathfrak p}:X longrightarrow mathfrak p$\u0000 where \u0000$mathfrak g=mathfrak k oplus mathfrak p$\u0000 is a Cartan decomposition of \u0000$mathfrak g$\u0000 . In this paper, we describe compact orbits of parabolic subgroups of G in terms of the gradient map \u0000$mu _{mathfrak p}$\u0000 .","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"247 1","pages":"615 - 623"},"PeriodicalIF":0.8,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43646940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Motivated by a new conjecture on the behavior of bricks, we start a systematic study of minimal $tau $ -tilting infinite (min- $tau $ -infinite, for short) algebras. In particular, we treat min- $tau $ -infinite algebras as a modern counterpart of minimal representation-infinite algebras and show some of the fundamental similarities and differences between these families. We then relate our studies to the classical tilting theory and observe that this modern approach can provide fresh impetus to the study of some old problems. We further show that in order to verify the conjecture, it is sufficient to treat those min- $tau $ -infinite algebras where almost all bricks are faithful. Finally, we also prove that minimal extending bricks have open orbits, and consequently obtain a simple proof of the brick analogue of the first Brauer–Thrall conjecture, recently shown by Schroll and Treffinger using some different techniques.
{"title":"MINIMAL ( \u0000$tau $\u0000 -)TILTING INFINITE ALGEBRAS","authors":"Kaveh Mousavand, Charles Paquette","doi":"10.1017/nmj.2022.28","DOIUrl":"https://doi.org/10.1017/nmj.2022.28","url":null,"abstract":"Abstract Motivated by a new conjecture on the behavior of bricks, we start a systematic study of minimal \u0000$tau $\u0000 -tilting infinite (min- \u0000$tau $\u0000 -infinite, for short) algebras. In particular, we treat min- \u0000$tau $\u0000 -infinite algebras as a modern counterpart of minimal representation-infinite algebras and show some of the fundamental similarities and differences between these families. We then relate our studies to the classical tilting theory and observe that this modern approach can provide fresh impetus to the study of some old problems. We further show that in order to verify the conjecture, it is sufficient to treat those min- \u0000$tau $\u0000 -infinite algebras where almost all bricks are faithful. Finally, we also prove that minimal extending bricks have open orbits, and consequently obtain a simple proof of the brick analogue of the first Brauer–Thrall conjecture, recently shown by Schroll and Treffinger using some different techniques.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"249 1","pages":"221 - 238"},"PeriodicalIF":0.8,"publicationDate":"2021-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42226505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We study fundamental properties of analytic K-theory of Tate rings such as homotopy invariance, Bass fundamental theorem, Milnor excision, and descent for admissible coverings.
{"title":"K-THEORY OF NON-ARCHIMEDEAN RINGS II","authors":"M. Kerz, S. Saito, Georg Tamme","doi":"10.1017/nmj.2023.4","DOIUrl":"https://doi.org/10.1017/nmj.2023.4","url":null,"abstract":"Abstract We study fundamental properties of analytic K-theory of Tate rings such as homotopy invariance, Bass fundamental theorem, Milnor excision, and descent for admissible coverings.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"251 1","pages":"669 - 685"},"PeriodicalIF":0.8,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41667476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We show that the Specht ideal of a two-rowed partition is perfect over an arbitrary field, provided that the characteristic is either zero or bounded below by the size of the second row of the partition, and we show this lower bound is tight. We also establish perfection and other properties of certain variants of Specht ideals, and find a surprising connection to the weak Lefschetz property. Our results, in particular, give a self-contained proof of Cohen–Macaulayness of certain h-equals sets, a result previously obtained by Etingof–Gorsky–Losev over the complex numbers using rational Cherednik algebras.
{"title":"PRINCIPAL RADICAL SYSTEMS, LEFSCHETZ PROPERTIES, AND PERFECTION OF SPECHT IDEALS OF TWO-ROWED PARTITIONS","authors":"Chris McDaniel, J. Watanabe","doi":"10.1017/nmj.2021.17","DOIUrl":"https://doi.org/10.1017/nmj.2021.17","url":null,"abstract":"Abstract We show that the Specht ideal of a two-rowed partition is perfect over an arbitrary field, provided that the characteristic is either zero or bounded below by the size of the second row of the partition, and we show this lower bound is tight. We also establish perfection and other properties of certain variants of Specht ideals, and find a surprising connection to the weak Lefschetz property. Our results, in particular, give a self-contained proof of Cohen–Macaulayness of certain h-equals sets, a result previously obtained by Etingof–Gorsky–Losev over the complex numbers using rational Cherednik algebras.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"247 1","pages":"690 - 730"},"PeriodicalIF":0.8,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46927754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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