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Quillen metric for singular families of Riemann surfaces with cusps and compact perturbation theorem 有尖点的黎曼曲面奇异族的奎伦度量和紧凑扰动定理
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-07-17 DOI: 10.4310/mrl.2023.v30.n6.a3
Siarhei Finski
{"title":"Quillen metric for singular families of Riemann surfaces with cusps and compact perturbation theorem","authors":"Siarhei Finski","doi":"10.4310/mrl.2023.v30.n6.a3","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n6.a3","url":null,"abstract":"We study the behavior of the Quillen metric for families of Riemann surfaces with hyperbolic cusps when the additional cusps are created by degeneration. More precisely, in our previous paper, we’ve shown that the renormalization of the Quillen metric associated with a family of Riemann surfaces with cusps extends continuously over the locus of singular curves. Here we show that modulo some explicit universal constant, this continuous extension coincides with the Quillen metric of the normalization of singular curves. As a consequence, we get an explicit relation in terms of the Bott–Chern classes between the Quillen metric associated with a metric with cusps and the Quillen metric associated with a metric on the compactified Riemann surface. We also prove compatibility between our version of the analytic torsion and the version of Takhtajan–Zograf, defined through lengths of closed geodesics.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745088","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
An ordinary rank-two case of local-global compatibility for automorphic representations of arbitrary weight over CM fields CM 场上任意权重的自动表征的局部-全局兼容性的普通秩二级情况
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-07-17 DOI: 10.4310/mrl.2023.v30.n6.a11
Yuji Yang
{"title":"An ordinary rank-two case of local-global compatibility for automorphic representations of arbitrary weight over CM fields","authors":"Yuji Yang","doi":"10.4310/mrl.2023.v30.n6.a11","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n6.a11","url":null,"abstract":"We prove a rank-two potential automorphy theorem for $mod l$ representations satisfying an ordinary condition. Combined with an ordinary automorphy lifting theorem from $href{https://doi.org/10.4007/annals.2023.197.3.2}{textrm{[1]}}$, we prove a rank-two, $p neq l$ case of local-global compatibility for regular algebraic cuspidal automorphic representations of arbitrary weight over CM fields that is $iota$-ordinary for some $overline{mathbb{Q}}_l tilde{to} mathbb{C}$.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745094","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
Uniqueness of equivariant harmonic maps to symmetric spaces and buildings 对称空间和建筑物的等效调和映射的唯一性
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-07-17 DOI: 10.4310/mrl.2023.v30.n6.a1
Georgios Daskalopoulos, Chikako Mese
{"title":"Uniqueness of equivariant harmonic maps to symmetric spaces and buildings","authors":"Georgios Daskalopoulos, Chikako Mese","doi":"10.4310/mrl.2023.v30.n6.a1","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n6.a1","url":null,"abstract":"We prove uniqueness of equivariant harmonic maps into irreducible symmetric spaces of non-compact type and Bruhat–Tits buildings associated to isometric actions by Zariski dense subgroups.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744902","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
Global well-posedness and scattering of 3D defocusing, cubic Schrödinger equation 三维散焦立方薛定谔方程的全局拟合与散射
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-07-17 DOI: 10.4310/mrl.2023.v30.n6.a10
Jia Shen, Yifei Wu
{"title":"Global well-posedness and scattering of 3D defocusing, cubic Schrödinger equation","authors":"Jia Shen, Yifei Wu","doi":"10.4310/mrl.2023.v30.n6.a10","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n6.a10","url":null,"abstract":"In this paper, we study the global well-posedness and scattering of 3D defocusing, cubic Schrödinger equation. Recently, Dodson $href{https://dx.doi.org/10.4171/RMI/1295}{textrm{[16]}}$ studied the global well-posedness in a critical Sobolev space $dot{W}^{11/7,7/6}$. In this paper, we aim to show that if the initial data belongs to $dot{H}^{frac{1}{2}}$ to guarantee the local existence, then some extra weak space which is supercritical, is sufficient to prove the global well-posedness. More precisely, we prove that if the initial data belongs to $dot{H}^{1/2} cap dot{W}^{s,1}$ for $12/13 lt s leqslant 1$, then the corresponding solution exists globally and scatters.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745100","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
Gluck twists on concordant or homotopic spheres 协球或同位球上的格鲁克捻转
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-07-17 DOI: 10.4310/mrl.2023.v30.n6.a6
Daniel Kasprowski, Mark Powell, Arunima Ray
{"title":"Gluck twists on concordant or homotopic spheres","authors":"Daniel Kasprowski, Mark Powell, Arunima Ray","doi":"10.4310/mrl.2023.v30.n6.a6","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n6.a6","url":null,"abstract":"Let $M$ be a compact 4-manifold and let $S$ and $T$ be embedded $2$-spheres in $M$, both with trivial normal bundle. We write $M_{S}$ and $M_T$ for the 4-manifolds obtained by the Gluck twist operation on $M$ along $S$ and $T$ respectively. We show that if $S$ and $T$ are concordant, then $M_S$ and $M_T$ are $s$-cobordant, and so if $pi_1(M)$ is good, then $M_S$ and $M_T$ are homeomorphic. Similarly, if $S$ and $T$ are homotopic then we show that $M_S$ and $M_T$ are simple homotopy equivalent.Under some further assumptions, we deduce th $M_S$ and $M_T$ are homeomorphic. We show that additional assumptions are necessary by giving an example where $S$ and $T$ are homotopic but $M_S$ and $M_T$ are not homeomorphic. We also give an example where $S$ and $T$ are homotopic and $M_S$ and $M_T$ are homeomorphic but not diffeomorphic.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745091","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
Special solutions to the Type IIA flow IIA 型气流的特殊解决方案
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-07-17 DOI: 10.4310/mrl.2023.v30.n6.a8
Alberto Raffero
{"title":"Special solutions to the Type IIA flow","authors":"Alberto Raffero","doi":"10.4310/mrl.2023.v30.n6.a8","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n6.a8","url":null,"abstract":"We consider the source-free Type IIA flow introduced by Fei–Phong–Picard–Zhang $href{https://dx.doi.org/10.4310/CJM.2021.v9.n3.a3}{textrm{[10]}}$, and we study it in the case where the relevant geometric datum is a symplectic half-flat SU(3)-structure. We show the existence of ancient, immortal and eternal solutions to the flow, provided that the initial symplectic half-flat structure satisfies suitable properties. In particular, we prove that the solution starting at a symplectic half-flat structure with Hermitian Ricci tensor is ancient and evolves self-similarly by scaling the initial datum. These results apply to all known (locally) homogeneous spaces admitting invariant symplectic half-flat SU(3)-structures.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745098","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
On numerically trivial automorphisms of threefolds of general type 论一般类型三褶的数值琐碎自形
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-07-17 DOI: 10.4310/mrl.2023.v30.n6.a5
Zhi Jiang, Wenfei Liu, Hang Zhao
{"title":"On numerically trivial automorphisms of threefolds of general type","authors":"Zhi Jiang, Wenfei Liu, Hang Zhao","doi":"10.4310/mrl.2023.v30.n6.a5","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n6.a5","url":null,"abstract":"$defAutQx{mathrm{Aut}_mathbb{Q}(X)}$ In this paper, we prove that the group $AutQx$ of numerically trivial automorphisms are uniformly bounded for smooth projective threefolds X of general type which either satisfy $q(X) geq 3$ or have a Gorenstein minimal model. If X is furthermore of maximal Albanese dimension, then $lvert AutQx rvert leq 4$, and the equality can be achieved by an unbounded family of threefolds previously constructed by the third author. Along the way we prove a Noether type inequality for log canonical pairs of general type with the coefficients of the boundary divisor from a given subset $mathcal{C} subset (0, 1]$ such that $mathcal{C} cup {1}$ attains the minimum.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745090","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
$p$-complete arc-descent for perfect complexes over integral perfectoid rings 积分完形环上完形复数的p$完全弧降
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-07-17 DOI: 10.4310/mrl.2023.v30.n6.a4
Kazuhiro Ito
{"title":"$p$-complete arc-descent for perfect complexes over integral perfectoid rings","authors":"Kazuhiro Ito","doi":"10.4310/mrl.2023.v30.n6.a4","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n6.a4","url":null,"abstract":"We prove $p$-complete arc-descent results for finite projective modules and perfect complexes over integral perfectoid rings.Using our resul,we clarify a reduction argument in the proof of the classification of $p$-divisible groups over integral perfectoid rings given by Scholze–Weinstein.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745089","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
Balanced hyperbolic and divisorially hyperbolic compact complex manifolds 平衡双曲和分裂双曲紧凑复流形
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-07-17 DOI: 10.4310/mrl.2023.v30.n6.a7
Samir Marouani, Dan Popovici
{"title":"Balanced hyperbolic and divisorially hyperbolic compact complex manifolds","authors":"Samir Marouani, Dan Popovici","doi":"10.4310/mrl.2023.v30.n6.a7","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n6.a7","url":null,"abstract":"We introduce two notions of hyperbolicity for not necessarily Kähler $n$-dimensional compact complex manifolds $X$. The first, called <i>balanced hyperbolicity</i>, generalises Gromov’s Kähler hyperbolicity by means of Gauduchon’s balanced metrics. The second, called <i>divisorial hyperbolicity</i>, generalises the Brody hyperbolicity by ruling out the existence of non-degenerate holomorphic maps from $mathbb{C}^{n-1}$ to $X$ that have what we term a subexponential growth. Our main result in the first part of the paper asserts that every balanced hyperbolic $X$ is also divisorially hyperbolic. We provide a certain number of examples and counter-examples and discuss various properties of these manifolds. In the second part of the paper, we introduce the notions of <i>divisorially Kähler</i> and <i>divisorially nef</i> real De Rham cohomology classes of degree $2$ and study their properties. They also apply to $C^infty$, not necessarily holomorphic, complex line bundles and are expected to be implied in certain cases by the hyperbolicity properties introduced in the first part of the work. While motivated by the observation of hyperbolicity properties of certain non-Kähler manifolds, all these four new notions seem to have a role to play even in the Kähler and the projective settings.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745092","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
Parametrized Kähler class and Zariski dense orbital 1-cohomology 参数化凯勒类和扎里斯基密集轨道 1-同调
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-07-17 DOI: 10.4310/mrl.2023.v30.n6.a9
Filippo Sarti, Alessio Savini
{"title":"Parametrized Kähler class and Zariski dense orbital 1-cohomology","authors":"Filippo Sarti, Alessio Savini","doi":"10.4310/mrl.2023.v30.n6.a9","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n6.a9","url":null,"abstract":"Let $Gamma$ be a finitely generated group and let $(X,mu_X)$ be an ergodic standard Borel probability $Gamma$-space. Suppose that $mathcal{X}$ is a Hermitian symmetric space not of tube type and assume that $G=operatorname{Isom}(mathcal{X})^{circ}$ is simple. Given a Zariski dense measurable cocycle $sigma:Gamma times X to G$, we define the notion of parametrized Kähler class and we show that it completely determines the cocycle up to cohomology.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745093","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
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