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Illinois Journal of Mathematics最新文献

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On the geometry of the Heisenberg group with a balanced metric 平衡度规下海森堡群的几何
IF 0.6
Illinois Journal of Mathematics Pub Date : 2023-04-01 DOI: 10.1215/00192082-10407050
Fidelis Bittencourt, Edson S. Figueiredo, Pedro Fusieger, J. Ripoll
{"title":"On the geometry of the Heisenberg group with a balanced metric","authors":"Fidelis Bittencourt, Edson S. Figueiredo, Pedro Fusieger, J. Ripoll","doi":"10.1215/00192082-10407050","DOIUrl":"https://doi.org/10.1215/00192082-10407050","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44649742","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
Genuinely ramified maps and pseudo-stable vector bundles 真分支映射与伪稳定向量丛
IF 0.6
Illinois Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.1215/00192082-10817494
I. Biswas, A. J. Parameswaran
{"title":"Genuinely ramified maps and pseudo-stable vector bundles","authors":"I. Biswas, A. J. Parameswaran","doi":"10.1215/00192082-10817494","DOIUrl":"https://doi.org/10.1215/00192082-10817494","url":null,"abstract":"Let $X$ and $Y$ be irreducible normal projective varieties, of same dimension, defined over an algebraically closed field, and let $f : Y rightarrow X$ be a finite generically smooth morphism such that the corresponding homomorphism between the 'etale fundamental groups $f_*:pi^{rm et}_{1}(Y) rightarrowpi^{rm et}_{1}(X)$ is surjective. Fix a polarization on $X$ and equip $Y$ with the pulled back polarization. For a point $y_0in Y$, let $varpi(Y, y_0)$ (respectively, $varpi(X, f(y_0))$) be the affine group scheme given by the neutral Tannakian category defined by the strongly pseudo-stable vector bundles of degree zero on $Y$ (respectively, $X$). We prove that the homomorphism $varpi(Y, y_0) rightarrow varpi(X, f(y_0))$ induced by $f$ is surjective. Let $E$ be a pseudo-stable vector bundle on $X$ and $F subset f^*E$ a pseudo-stable subbundle with $mu(F)= mu(f^*E)$. We prove that $f^*E$ is pseudo-stable and there is a pseudo-stable subbundle $W subset E$ such that $f^*W = F$ as subbundles of $f^*E$.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48258547","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
Toeplitz–Berezin-type symbols and solutions of some operator equations Toeplitz–Berezin型符号与一些算子方程的解
IF 0.6
Illinois Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.1215/00192082-10597073
M. Garayev, H. Guediri, Houcine Sadraoui
{"title":"Toeplitz–Berezin-type symbols and solutions of some operator equations","authors":"M. Garayev, H. Guediri, Houcine Sadraoui","doi":"10.1215/00192082-10597073","DOIUrl":"https://doi.org/10.1215/00192082-10597073","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48688641","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
Spherical CR-symmetric hypersurfaces in Hermitian symmetric spaces Hermitian对称空间中的球面CR对称超曲面
IF 0.6
Illinois Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.1215/00192082-10817210
Jong Taek Cho, M. Kimura
{"title":"Spherical CR-symmetric hypersurfaces in Hermitian symmetric spaces","authors":"Jong Taek Cho, M. Kimura","doi":"10.1215/00192082-10817210","DOIUrl":"https://doi.org/10.1215/00192082-10817210","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43725269","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
Discrete multilinear maximal functions and number theory 离散多线性极大函数与数论
IF 0.6
Illinois Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.1215/00192082-10817246
T. Anderson
{"title":"Discrete multilinear maximal functions and number theory","authors":"T. Anderson","doi":"10.1215/00192082-10817246","DOIUrl":"https://doi.org/10.1215/00192082-10817246","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47734123","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
Variance of squarefull numbers in short intervals 平方数在短间隔内的方差
Illinois Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.1215/00192082-10972707
Tsz Ho Chan
{"title":"Variance of squarefull numbers in short intervals","authors":"Tsz Ho Chan","doi":"10.1215/00192082-10972707","DOIUrl":"https://doi.org/10.1215/00192082-10972707","url":null,"abstract":"In this paper, we study the variance of the number of squarefull numbers in short intervals. As a result, we are able to prove that, for any $0<theta<1/2$, almost all short intervals $(x, x + x^{1/2 + theta}]$ contain about $frac{zeta(3/2)}{2 zeta(3)} x^theta$ squarefull numbers.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"273 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":"135509001","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
Lefschetz numbers of Verdier monodromy and the motivic monodromy conjecture for toric varieties 环型变异的Verdier单态的Lefschetz数和动机单态猜想
Illinois Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.1215/00192082-10950709
Jen-Chieh Hsiao
{"title":"Lefschetz numbers of Verdier monodromy and the motivic monodromy conjecture for toric varieties","authors":"Jen-Chieh Hsiao","doi":"10.1215/00192082-10950709","DOIUrl":"https://doi.org/10.1215/00192082-10950709","url":null,"abstract":"We give an expression of the Lefschetz number of iterates of the Verdier monodormy associated to an ideal on a complex algebraic variety in terms of the Euler characteristic of a space of truncated arcs. This extends the result of Denef and Loeser in the case of principal ideal on a smooth variety, and motivates a definition of motivic Milnor fiber for ideals. A discussion of the monodromy conjecture for motivic zeta functions of torus-invariant ideals on toric varieties is also included.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"35 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":"135604122","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
Ore localization of amenable monoid actions and applications toward entropy—addition formulas and the bridge theorem 可服从单形动作的局部化及其在熵加公式和桥定理中的应用
Illinois Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.1215/00192082-10950854
Dikran Dikranjan, Anna Giordano Bruno, Simone Virili
{"title":"Ore localization of amenable monoid actions and applications toward entropy—addition formulas and the bridge theorem","authors":"Dikran Dikranjan, Anna Giordano Bruno, Simone Virili","doi":"10.1215/00192082-10950854","DOIUrl":"https://doi.org/10.1215/00192082-10950854","url":null,"abstract":"For a left action $Soverset{lambda}{curvearrowright}X$ of a cancellative right amenable monoid $S$ on a discrete Abelian group $X$, we construct its Ore localization $Goverset{lambda^*}{curvearrowright}X^*$, where $G$ is the group of left fractions of $S$; analogously, for a right action $Koverset{rho}curvearrowleft S$ on a compact space $K$, we construct its Ore colocalization $K^*overset{rho^*}{curvearrowleft} G$. Both constructions preserve entropy, i.e., for the algebraic entropy $h_{mathrm{alg}}$ and for the topological entropy $h_{mathrm{top}}$ one has $h_{mathrm{alg}}(lambda)=h_{mathrm{alg}}(lambda^*)$ and $h_{mathrm{top}}(rho)=h_{mathrm{top}}(rho^*)$, respectively. Exploiting these constructions and the theory of quasi-tilings, we extend the Addition Theorem for $h_{mathrm{top}}$, known for right actions of countable amenable groups on compact metrizable groups, to right actions $Koverset{rho}{curvearrowleft} S$ of cancellative right amenable monoids $S$ (with no restrictions on the cardinality) on arbitrary compact groups $K$. When the compact group $K$ is Abelian, we prove that $h_{mathrm{top}}(rho)$ coincides with $h_{mathrm{alg}}(hat{rho})$, where $Soverset{hat{rho}}curvearrowright X$ is the dual left action on the discrete Pontryagin dual $X=hat{K}$, that is, a so-called Bridge Theorem. From the Addition Theorem for $h_{mathrm{top}}$ and the Bridge Theorem, we obtain an Addition Theorem for $h_{mathrm{alg}}$ for left actions $Soverset{lambda}curvearrowright X$ on discrete Abelian groups, so far known only under the hypotheses that either $X$ is torsion or $S$ is locally monotileable. The proofs substantially use the unified approach towards entropy based on the entropy of actions of cancellative right amenable monoids on appropriately defined normed monoids.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"418 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":"135509003","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
Multiparameter ergodic theorems of Abelian type for power-bounded operators 幂有界算子的Abel型多参数遍历定理
IF 0.6
Illinois Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.1215/00192082-10817368
T. Yoshimoto
{"title":"Multiparameter ergodic theorems of Abelian type for power-bounded operators","authors":"T. Yoshimoto","doi":"10.1215/00192082-10817368","DOIUrl":"https://doi.org/10.1215/00192082-10817368","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43748757","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
Direct hyperfinite representations of finitely additive probabilities 有限可加概率的直接超有限表示
Illinois Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.1215/00192082-10908708
Maxwell B. Stinchcombe
{"title":"Direct hyperfinite representations of finitely additive probabilities","authors":"Maxwell B. Stinchcombe","doi":"10.1215/00192082-10908708","DOIUrl":"https://doi.org/10.1215/00192082-10908708","url":null,"abstract":"Fix a standard measurable space (X,X) and an internal, hyperfinite H⊂∗X that contains each x∈X. All finitely additive probabilities on (X,X) can be represented by setting p(B) equal to the standard part of Q(∗B∩H) for some internal probability Q supported on H. From this starting point, we have the following: a decomposition of two ways in which a probability can fail to be countably additive, a nonstandard characterization of countable additivity for probabilities on complete separable metic spaces, and results on the multiplicity of hyperfinitely supported probabilities that represent a given finitely additive p, from which we have set-valued integrals with respect to products of finitely additive probabilities that respect statistical independence, and for subfields or sub-σ-fields of X, a proper ∗X-based disintegration of finitely additive probabilities as a countably additive integral over the set of finitely additive probabilities. We end with several applications for which the alternative Stone space approach to representing finitely additive probabilities is an impediment to the analyses.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"23 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":"135609918","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
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