{"title":"On the Rigidity of Some Extensions of Domains","authors":"Dayan Liu, Xiaosong Sun","doi":"10.1307/mmj/20205957","DOIUrl":"https://doi.org/10.1307/mmj/20205957","url":null,"abstract":"","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89560978","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}
{"title":"Coarse Z-Boundaries for Groups","authors":"C. Guilbault, Molly A. Moran","doi":"10.1307/mmj/20206001","DOIUrl":"https://doi.org/10.1307/mmj/20206001","url":null,"abstract":". We generalize Bestvina’s notion of a Z -boundary for a group to that of a “coarse Z -boundary.” We show that established theorems about Z -boundaries carry over nicely to the more general theory, and that some wished-for properties of Z -boundaries become theorems when applied to coarse Z -boundaries. Most notably, the property of admitting a coarse Z -boundary is a pure quasi-isometry invariant. In the process, we streamline both new and existing definitions by in-troducing the notion of a “model Z -geometry.” In accordance with the existing theory, we also develop an equivariant version of the above—that of a “coarse E Z -boundary.”","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72466181","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}
{"title":"Canonical Modules and Class Groups of Rees-Like Algebras","authors":"P. Mantero, J. McCullough, L. Miller","doi":"10.1307/mmj/20205974","DOIUrl":"https://doi.org/10.1307/mmj/20205974","url":null,"abstract":"Rees-like algebras have played a major role in settling the EisenbudGoto conjecture. This article concerns the structure of the canonical module of the Rees-like algebra and its class groups. Via an explicit computation based on linkage, we provide an explicit and surprisingly well-structured resolution of the canonical module in terms of a type of double-Koszul complex. Additionally, we give descriptions of both the divisor class group and the Picard group of a Rees-like algebra.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82949288","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}
{"title":"Pseudo-Néron Model and Restriction of Sections","authors":"Santai Qu","doi":"10.1307/mmj/20195764","DOIUrl":"https://doi.org/10.1307/mmj/20195764","url":null,"abstract":"","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90769718","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}
{"title":"A Note on the Concordance Z-Genus","authors":"Allison N. Miller, Junghwan Park","doi":"10.1307/mmj/20216070","DOIUrl":"https://doi.org/10.1307/mmj/20216070","url":null,"abstract":"","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88341389","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}
{"title":"Product Theorem on Delta Invariants via Adding a General Boundary","authors":"Chuyu Zhou","doi":"10.1307/mmj/20205993","DOIUrl":"https://doi.org/10.1307/mmj/20205993","url":null,"abstract":". It’s well-known that adding a general boundary would create K-stability. As an application, we reprove product theorem for delta invariants of Fano varieties.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79649187","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}
{"title":"The dlt Motivic Zeta Function Is Not Well Defined","authors":"J. Nicaise, Naud Potemans, W. Veys","doi":"10.1307/mmj/20216148","DOIUrl":"https://doi.org/10.1307/mmj/20216148","url":null,"abstract":"In arXiv:1408.4708, Xu defines the dlt motivic zeta function associated to a regular function $f$ on a smooth variety $X$ over a field of characteristic zero. This is an adaptation of the classical motivic zeta function that was introduced by Denef and Loeser. The dlt motivic zeta function is defined on a dlt modification via a Denef-Loeser-type formula, replacing classes of strata in the Grothendieck ring of varieties by stringy motives. We provide explicit examples that show that the dlt motivic zeta function depends on the choice of dlt modification, contrary to what is claimed in arXiv:1408.4708, and that it is therefore not well-defined.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72752589","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}
{"title":"Uniqueness of Conformal Measures and Local Mixing for Anosov Groups","authors":"Sam O. Edwards, Minju M. Lee, H. Oh","doi":"10.1307/mmj/20217222","DOIUrl":"https://doi.org/10.1307/mmj/20217222","url":null,"abstract":"Abstract. In the late seventies, Sullivan showed that for a convex cocompact subgroup Γ of SO(n, 1) with critical exponent δ > 0, any Γ-conformal measure on ∂H of dimension δ is necessarily supported on the limit set Λ and that the conformal measure of dimension δ exists uniquely. We prove an analogue of this theorem for any Zariski dense Anosov subgroup Γ of a connected semisimple real algebraic group G of rank at most 3. We also obtain the local mixing for generalized BMS measures on ΓG including Haar measures.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73273864","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}