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Approximation by BV-extension Sets via Perimeter Minimization in Metric Spaces 通过公设空间中的周长最小化用 BV 扩展集进行逼近
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-03-22 DOI: 10.1093/imrn/rnae048
Jesse Koivu, Danka Lučić, Tapio Rajala
{"title":"Approximation by BV-extension Sets via Perimeter Minimization in Metric Spaces","authors":"Jesse Koivu, Danka Lučić, Tapio Rajala","doi":"10.1093/imrn/rnae048","DOIUrl":"https://doi.org/10.1093/imrn/rnae048","url":null,"abstract":"We show that every bounded domain in a metric measure space can be approximated in measure from inside by closed $BV$-extension sets. The extension sets are obtained by minimizing the sum of the perimeter and the measure of the difference between the domain and the set. By earlier results, in PI spaces the minimizers have open representatives with locally quasiminimal surface. We give an example in a PI space showing that the open representative of the minimizer need not be a $BV$-extension domain nor locally John.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":"21 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201301","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}
引用次数: 0
Maximality Properties of Generalized Springer Representations of SO (N, ℂ) SO (N, ℂ)的广义斯普林格表示的最大值特性
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-03-20 DOI: 10.1093/imrn/rnae041
Ruben La
{"title":"Maximality Properties of Generalized Springer Representations of SO (N, ℂ)","authors":"Ruben La","doi":"10.1093/imrn/rnae041","DOIUrl":"https://doi.org/10.1093/imrn/rnae041","url":null,"abstract":"Let $C$ be a unipotent class of $G=textrm{SO}(N,mathbb{C})$, $mathcal{E}$ an irreducible $G$-equivariant local system on $C$. The generalized Springer representation $rho (C,mathcal{E})$ appears in the top cohomology of some variety. Let $bar rho (C,mathcal{E})$ be the representation obtained by summing over all cohomology groups of this variety. It is well known that $rho (C,mathcal{E})$ appears in $bar rho (C,mathcal{E})$ with multiplicity $1$ and that its Springer support $C$ is strictly minimal in the closure ordering among the Springer supports of the irreducbile subrepresentations of $bar rho (C,mathcal{E})$. Suppose $C$ is parametrized by an orthogonal partition with only odd parts. We prove that $bar rho (C,mathcal{E})$ (resp. $textrm{sgn}otimes bar rho (C,mathcal{E})$) has a unique multiplicity 1 “maximal” subrepresentation $rho ^{textrm{max}}$ (resp. “minimal” subrepresentation $textrm{sgn}otimes rho ^{textrm{max}}$), where $textrm{sgn}$ is the sign representation. These are analogues of results for $textrm{Sp}(2n,mathbb{C})$ by Waldspurger.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":"20 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201344","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}
引用次数: 0
Determinantal Representations and the Image of the Principal Minor Map 主小地图的确定性表示和图像
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-03-20 DOI: 10.1093/imrn/rnae038
Abeer Al Ahmadieh, Cynthia Vinzant
{"title":"Determinantal Representations and the Image of the Principal Minor Map","authors":"Abeer Al Ahmadieh, Cynthia Vinzant","doi":"10.1093/imrn/rnae038","DOIUrl":"https://doi.org/10.1093/imrn/rnae038","url":null,"abstract":"In this paper we explore determinantal representations of multiaffine polynomials and consequences for the image of various spaces of matrices under the principal minor map. We show that a real multiaffine polynomial has a definite Hermitian determinantal representation if and only if all of its so-called Rayleigh differences factor as Hermitian squares and use this characterization to conclude that the image of the space of Hermitian matrices under the principal minor map is cut out by the orbit of finitely many equations and inequalities under the action of $(textrm{SL}_{2}(mathbb{R}))^{n} rtimes S_{n}$. We also study such representations over more general fields with quadratic extensions. Factorizations of Rayleigh differences prove an effective tool for capturing subtle behavior of the principal minor map. In contrast to the Hermitian case, we give examples to show for any field $mathbb{F}$, there is no finite set of equations whose orbit under $(textrm{SL}_{2}(mathbb{F}))^{n} rtimes S_{n}$ cuts out the image of $ntimes n$ matrices over ${mathbb{F}}$ under the principal minor map for every $n$.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":"162 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201297","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}
引用次数: 0
Drinfeld’s Lemma for F-isocrystals, I F-isocrystal 的 Drinfeld 定理，I
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-03-15 DOI: 10.1093/imrn/rnae039
Kiran S Kedlaya
{"title":"Drinfeld’s Lemma for F-isocrystals, I","authors":"Kiran S Kedlaya","doi":"10.1093/imrn/rnae039","DOIUrl":"https://doi.org/10.1093/imrn/rnae039","url":null,"abstract":"We prove that in either the convergent or overconvergent setting, an absolutely irreducible $F$-isocrystal on the absolute product of two or more smooth schemes over perfect fields of characteristic $p$, further equipped with actions of the partial Frobenius maps, is an external product of $F$-isocrystals over the multiplicands. The corresponding statement for lisse $overline{{mathbb{Q}}}_{ell }$-sheaves, for $ell neq p$ a prime, is a consequence of Drinfeld’s lemma on the fundamental groups of absolute products of schemes in characteristic $p$. The latter plays a key role in V. Lafforgue’s approach to the Langlands correspondence for reductive groups with $ell $-adic coefficients; the $p$-adic analogue will be considered in subsequent work with Daxin Xu.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":"21 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140147473","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}
引用次数: 0
Birational Transformations on Irreducible Compact Hermitian Symmetric Spaces 不可还原紧凑赫尔米特对称空间上的双向变换
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-03-15 DOI: 10.1093/imrn/rnae045
Cong Ding
{"title":"Birational Transformations on Irreducible Compact Hermitian Symmetric Spaces","authors":"Cong Ding","doi":"10.1093/imrn/rnae045","DOIUrl":"https://doi.org/10.1093/imrn/rnae045","url":null,"abstract":"We construct a sequence of explicit blow-ups and blow-downs on an irreducible compact Hermitian symmetric spaces $X$ which transforms it into a projective space of the same dimension. Moreover, this resolves a birational map given by Landsberg and Manivel. Centers of the blow-ups for $X$ are constructed by loci of chains of minimal rational curves and centers of the blow-ups for the projective space are constructed from the variety of minimal rational tangents of $X$ and its higher secant varieties. The result was known in the special case where $X$ is of rank 2 and could be found in Zak’s monograph “Tangents and secants of algebraic varieties.”","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":"18 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140147458","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}
引用次数: 0
Bounds for Rational Points on Algebraic Curves, Optimal in the Degree, and Dimension Growth 代数曲线上有理点的边界、度数最优和维数增长
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-03-05 DOI: 10.1093/imrn/rnae034
Gal Binyamini, Raf Cluckers, Dmitry Novikov
{"title":"Bounds for Rational Points on Algebraic Curves, Optimal in the Degree, and Dimension Growth","authors":"Gal Binyamini, Raf Cluckers, Dmitry Novikov","doi":"10.1093/imrn/rnae034","DOIUrl":"https://doi.org/10.1093/imrn/rnae034","url":null,"abstract":"Bounding the number of rational points of height at most $H$ on irreducible algebraic plane curves of degree $d$ has been an intense topic of investigation since the work by Bombieri and Pila. In this paper we establish optimal dependence on $d$ by showing the upper bound $C d^{2} H^{2/d} (log H)^{kappa }$ with some absolute constants $C$ and $kappa $. This bound is optimal with respect to both $d$ and $H$, except for the constants $C$ and $kappa $. This answers a question raised by Salberger, leading to a simplified proof of his results on the uniform dimension growth conjectures of Heath-Brown and Serre, and where at the same time we replace the $H^{varepsilon }$ factor by a power of $log H$. The main strength of our approach comes from the combination of a new, efficient form of smooth parametrizations of algebraic curves with a century-old criterion of Pólya, which allows us to save one extra power of $d$ compared with the standard approach using Bézout’s theorem.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":"271 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045140","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}
引用次数: 0
Rectifiability of Flat Singular Points for Area-Minimizing mod 2Q Hypercurrents 面积最小化模 2Q 超电流平奇点的可整流性
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-02-29 DOI: 10.1093/imrn/rnae024
Anna Skorobogatova
{"title":"Rectifiability of Flat Singular Points for Area-Minimizing mod 2Q Hypercurrents","authors":"Anna Skorobogatova","doi":"10.1093/imrn/rnae024","DOIUrl":"https://doi.org/10.1093/imrn/rnae024","url":null,"abstract":"Consider an $ m $-dimensional area minimizing mod$ (2Q) $ current $ T $, with $ Qin {mathbb {N}} $, inside a sufficiently regular Riemannian manifold of dimension $ m + 1 $. We show that the set of singular density-$ Q $ points with a flat tangent cone is $ (m-2) $-rectifiable. This complements the thorough structural analysis of the singularities of area-minimizing hypersurfaces modulo $ p $ that has been completed in the series of works of De Lellis–Hirsch–Marchese–Stuvard and De Lellis–Hirsch–Marchese–Stuvard–Spolaor, and the work of Minter–Wickramasekera.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":"17 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009964","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}
引用次数: 0
Differential Graded Manifolds of Finite Positive Amplitude 有限正振幅的差分分级流形
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-02-29 DOI: 10.1093/imrn/rnae023
Kai Behrend, Hsuan-Yi Liao, Ping Xu
{"title":"Differential Graded Manifolds of Finite Positive Amplitude","authors":"Kai Behrend, Hsuan-Yi Liao, Ping Xu","doi":"10.1093/imrn/rnae023","DOIUrl":"https://doi.org/10.1093/imrn/rnae023","url":null,"abstract":"We prove that dg manifolds of finite positive amplitude, that is, bundles of positively graded curved $L_{infty }[1]$-algebras, form a category of fibrant objects. As a main step in the proof, we obtain a factorization theorem using path spaces. First we construct an infinite-dimensional factorization of a diagonal morphism using actual path spaces motivated by the AKSZ construction. Then we cut down to finite dimensions using the Fiorenza-Manetti method. The main ingredient in our method is the homotopy transfer theorem for curved $L_{infty }[1]$-algebras. As an application, we study the derived intersections of manifolds.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":"72 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140010023","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}
引用次数: 0
Shuffle Algebras and Their Integral Forms: Specialization Map Approach in Types B n and G 2 Shuffle Algebras and Their Integral Forms：类型 B n 和 G 2 中的特化图方法
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-02-27 DOI: 10.1093/imrn/rnae029
Yue Hu, Alexander Tsymbaliuk
{"title":"Shuffle Algebras and Their Integral Forms: Specialization Map Approach in Types B n and G 2","authors":"Yue Hu, Alexander Tsymbaliuk","doi":"10.1093/imrn/rnae029","DOIUrl":"https://doi.org/10.1093/imrn/rnae029","url":null,"abstract":"We construct a family of PBWD (Poincaré-Birkhoff-Witt-Drinfeld) bases for the positive subalgebras of quantum loop algebras of type $B_{n}$ and $G_{2}$, as well as their Lusztig and RTT (for type $B_{n}$ only) integral forms, in the new Drinfeld realization. We also establish a shuffle algebra realization of these ${mathbb {Q}}(v)$-algebras (proved earlier in [26] by completely different tools) and generalize the latter to the above ${{mathbb {Z}}}[v,v^{-1}]$-forms. The rational counterparts provide shuffle algebra realizations of positive subalgebras of type $B_{n}$ and $G_{2}$ Yangians and their Drinfeld-Gavarini duals. All of this generalizes the type $A_{n}$ results of [30].","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":"19 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140010026","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}
引用次数: 0
Operator Space Complexification Transfigured 运算器空间的复杂化转换
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-02-26 DOI: 10.1093/imrn/rnae026
David P Blecher, Mehrdad Kalantar
{"title":"Operator Space Complexification Transfigured","authors":"David P Blecher, Mehrdad Kalantar","doi":"10.1093/imrn/rnae026","DOIUrl":"https://doi.org/10.1093/imrn/rnae026","url":null,"abstract":"Given a finite group $G$, a central subgroup $H$ of $G$, and an operator space $X$ equipped with an action of $H$ by complete isometries, we construct an operator space $X_{G}$ equipped with an action of $G$ that is unique under a “reasonable” condition. This generalizes the operator space complexification $X_{c}$ of $X$. As a linear space $X_{G}$ is the space obtained from inducing the representation of $H$ to $G$ (in the sense of Frobenius). Indeed a main achievement of our paper is the induced representation construction in the category of operator spaces. This has been hitherto elusive even for Banach spaces since it is not clear how to norm the induced space. We show that for a large class of group actions the induced space has a unique operator space norm.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":"32 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979116","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}
引用次数: 0
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