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Regular logarithmic connections.
IF 1.3 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2024-12-03 DOI: 10.1007/s00208-024-03047-9
Piotr Achinger
{"title":"Regular logarithmic connections.","authors":"Piotr Achinger","doi":"10.1007/s00208-024-03047-9","DOIUrl":"https://doi.org/10.1007/s00208-024-03047-9","url":null,"abstract":"<p><p>We introduce the notion of a regular integrable connection on a smooth log scheme over <math><mi>C</mi></math> and construct an equivalence between the category of such connections and the category of integrable connections on its analytification, compatible with de Rham cohomology. This extends the work of Deligne (when the log structure is trivial), and combined with the work of Ogus yields a topological description of the category of regular connections in terms of certain constructible sheaves on the Kato-Nakayama space. The key ingredients are the notion of a canonical extension in this context and the existence of good compactifications of log schemes obtained recently by Włodarczyk.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"391 4","pages":"5293-5339"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11954731/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143753555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generic solutions of equations involving the modular j function.
IF 1.3 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2025-01-08 DOI: 10.1007/s00208-024-03082-6
Sebastian Eterović
{"title":"Generic solutions of equations involving the modular <i>j</i> function.","authors":"Sebastian Eterović","doi":"10.1007/s00208-024-03082-6","DOIUrl":"https://doi.org/10.1007/s00208-024-03082-6","url":null,"abstract":"<p><p>Assuming a modular version of Schanuel's conjecture and the modular Zilber-Pink conjecture, we show that the existence of generic solutions of certain families of equations involving the modular <i>j</i> function can be reduced to the problem of finding a Zariski dense set of solutions. By imposing some conditions on the field of definition of the variety, we are also able to obtain versions of this result without relying on these conjectures, and even a result including the derivatives of <i>j</i>.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"391 4","pages":"6401-6449"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11954734/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143753525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Foliation adjunction. 叶片连接
IF 1.3 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2024-12-21 DOI: 10.1007/s00208-024-03067-5
Paolo Cascini, Calum Spicer
{"title":"Foliation adjunction.","authors":"Paolo Cascini, Calum Spicer","doi":"10.1007/s00208-024-03067-5","DOIUrl":"https://doi.org/10.1007/s00208-024-03067-5","url":null,"abstract":"<p><p>We present an adjunction formula for foliations on varieties and we consider applications of the adjunction formula to the cone theorem for rank one foliations and the study of foliation singularities.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"391 4","pages":"5695-5727"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11954749/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143753515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials.
IF 1.3 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2024-10-04 DOI: 10.1007/s00208-024-03011-7
Alexander Ulanovskii, Ilya Zlotnikov
{"title":"Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials.","authors":"Alexander Ulanovskii, Ilya Zlotnikov","doi":"10.1007/s00208-024-03011-7","DOIUrl":"https://doi.org/10.1007/s00208-024-03011-7","url":null,"abstract":"<p><p>We introduce two families of generators (functions) <math><mi>G</mi></math> that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results are proved on the density of separated sets that provide non-uniform sampling for the shift-invariant and quasi shift-invariant spaces generated by elements of these families. As an application, new sharp results are obtained on the density of semi-regular lattices for the Gabor frames generated by elements from these families.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"391 3","pages":"3429-3456"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11829847/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143441152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sequential topological complexity of aspherical spaces and sectional categories of subgroup inclusions.
IF 1.3 2区 数学
Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2024-11-09 DOI: 10.1007/s00208-024-03033-1
Arturo Espinosa Baro, Michael Farber, Stephan Mescher, John Oprea
{"title":"Sequential topological complexity of aspherical spaces and sectional categories of subgroup inclusions.","authors":"Arturo Espinosa Baro, Michael Farber, Stephan Mescher, John Oprea","doi":"10.1007/s00208-024-03033-1","DOIUrl":"https://doi.org/10.1007/s00208-024-03033-1","url":null,"abstract":"<p><p>We generalize results from topological robotics on the topological complexity (TC) of aspherical spaces to sectional categories of fibrations inducing subgroup inclusions on the level of fundamental groups. In doing so, we establish new lower bounds on sequential TCs of aspherical spaces as well as the parametrized TC of epimorphisms. Moreover, we generalize the Costa-Farber canonical class for TC to classes for sequential TCs and explore their properties. We combine them with the results on sequential TCs of aspherical spaces to obtain results on spaces that are not necessarily aspherical.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"391 3","pages":"4555-4605"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11829864/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143441159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Coarsely holomorphic curves and symplectic topology 粗全形曲线与交映拓扑学
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-09-19 DOI: 10.1007/s00208-024-02985-8
Spencer Cattalani
{"title":"Coarsely holomorphic curves and symplectic topology","authors":"Spencer Cattalani","doi":"10.1007/s00208-024-02985-8","DOIUrl":"https://doi.org/10.1007/s00208-024-02985-8","url":null,"abstract":"<p>A taming symplectic structure provides an upper bound on the area of an approximately pseudoholomorphic curve in terms of its homology class. We prove that, conversely, an almost complex manifold with such an area bound admits a taming symplectic structure. This confirms a speculation by Gromov. We also characterize the cone of taming symplectic structures numerically, prove that complex 2-cycles can be approximated by coarsely holomorphic curves, and provide a lower energy bound for such curves.\u0000</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"31 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248056","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
Multifractality and intermittency in the limit evolution of polygonal vortex filaments 多边形涡旋丝极限演化中的多分形和间歇性
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-09-17 DOI: 10.1007/s00208-024-02971-0
Valeria Banica, Daniel Eceizabarrena, Andrea R. Nahmod, Luis Vega
{"title":"Multifractality and intermittency in the limit evolution of polygonal vortex filaments","authors":"Valeria Banica, Daniel Eceizabarrena, Andrea R. Nahmod, Luis Vega","doi":"10.1007/s00208-024-02971-0","DOIUrl":"https://doi.org/10.1007/s00208-024-02971-0","url":null,"abstract":"<p>With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality and intermittency of the family of generalized Riemann’s non-differentiable functions </p><span>$$begin{aligned} R_{x_0}(t) = sum _{n ne 0} frac{e^{2pi i ( n^2 t + n x_0 ) } }{n^2}, qquad x_0 in [0,1]. end{aligned}$$</span><p>These functions represent, in a certain limit, the trajectory of regular polygonal vortex filaments that evolve according to the binormal flow. When <span>(x_0)</span> is rational, we show that <span>(R_{x_0})</span> is multifractal and intermittent by completely determining the spectrum of singularities of <span>(R_{x_0})</span> and computing the <span>(L^p)</span> norms of its Fourier high-pass filters, which are analogues of structure functions. We prove that <span>(R_{x_0})</span> has a multifractal behavior also when <span>(x_0)</span> is irrational. The proofs rely on a careful design of Diophantine sets that depend on <span>(x_0)</span>, which we study by using the Duffin–Schaeffer theorem and the Mass Transference Principle.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"11 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248055","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
On the uniqueness of periodic solutions for a Rayleigh–Liénard system with impulses 论带脉冲的 Rayleigh-Liénard 系统周期解的唯一性
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-09-17 DOI: 10.1007/s00208-024-02996-5
Hebai Chen, Jie Jin, Zhaoxia Wang, Dongmei Xiao
{"title":"On the uniqueness of periodic solutions for a Rayleigh–Liénard system with impulses","authors":"Hebai Chen, Jie Jin, Zhaoxia Wang, Dongmei Xiao","doi":"10.1007/s00208-024-02996-5","DOIUrl":"https://doi.org/10.1007/s00208-024-02996-5","url":null,"abstract":"<p>This paper is to provide a criterion of the uniqueness of periodic solutions for a Rayleigh-Liénard system with state-dependent impulses. Notice that such results of a planar system with state-dependent impulses are few. Moreover, the Rayleigh-Liénard system with state-dependent impulses has wide applications, such as a simple pendulum and a spring vibrator. Further, we obtain the uniqueness of periodic solutions of the simple pendulum with state-dependent impulses and the spring vibrator with state-dependent impulses by the criterion.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"85 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248053","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
Uniformly super McDuff $$hbox {II}_1$$ factors 统一超麦克杜夫 $$hbox {II}_1$$ 因子
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-09-12 DOI: 10.1007/s00208-024-02959-w
Isaac Goldbring, David Jekel, Srivatsav Kunnawalkam Elayavalli, Jennifer Pi
{"title":"Uniformly super McDuff $$hbox {II}_1$$ factors","authors":"Isaac Goldbring, David Jekel, Srivatsav Kunnawalkam Elayavalli, Jennifer Pi","doi":"10.1007/s00208-024-02959-w","DOIUrl":"https://doi.org/10.1007/s00208-024-02959-w","url":null,"abstract":"<p>We introduce and study the family of uniformly super McDuff <span>(hbox {II}_1)</span> factors. This family is shown to be closed under elementary equivalence and also coincides with the family of <span>(hbox {II}_1)</span> factors with the Brown property introduced in Atkinson et al. (Adv. Math. 396, 108107, 2022). We show that a certain family of existentially closed factors, the so-called infinitely generic factors, are uniformly super McDuff, thereby improving a recent result of Chifan et al. (Embedding Universality for <span>(hbox {II}_1)</span> Factors with Property (T). arXiv preprint, 2022). We also show that Popa’s family of strongly McDuff <span>(hbox {II}_1)</span> factors are uniformly super McDuff. Lastly, we investigate when finitely generic <span>(hbox {II}_1)</span> factors are uniformly super McDuff.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185182","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
Normalized solutions for Kirchhoff equations with Sobolev critical exponent and mixed nonlinearities 具有索波列夫临界指数和混合非线性的基尔霍夫方程的归一化解
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-09-12 DOI: 10.1007/s00208-024-02982-x
Sitong Chen, Xianhua Tang
{"title":"Normalized solutions for Kirchhoff equations with Sobolev critical exponent and mixed nonlinearities","authors":"Sitong Chen, Xianhua Tang","doi":"10.1007/s00208-024-02982-x","DOIUrl":"https://doi.org/10.1007/s00208-024-02982-x","url":null,"abstract":"<p>This paper focuses on the existence of normalized solutions for the following Kirchhoff equation: </p><span>$$begin{aligned} left{ begin{array}{ll} -left( a+bint _{{mathbb {R}}^3}|nabla u|^2textrm{d}xright) Delta u+lambda u=u^5+mu |u|^{q-2}u, &amp; xin {mathbb {R}}^3, int _{{mathbb {R}}^3}u^2textrm{d}x=c, end{array} right. end{aligned}$$</span><p>where <span>(a,b,c&gt;0)</span>, <span>(mu in {mathbb {R}})</span> and <span>(2&lt;q&lt;6)</span>, <span>(lambda in {mathbb {R}})</span> will arise as a Lagrange multiplier that is not a priori given. By using new analytical techniques, the paper establishes several existence results for the case <span>(mu &gt;0)</span>: </p><ol>\u0000<li>\u0000<span>(1)</span>\u0000<p>The existence of two solutions, one being a local minimizer and the other of mountain-pass type, under explicit conditions on <i>c</i> when <span>(2&lt;q&lt;frac{10}{3})</span>.</p>\u0000</li>\u0000<li>\u0000<span>(2)</span>\u0000<p>The existence of a mountain-pass type solution under explicit conditions on <i>c</i> when <span>(frac{10}{3}le q&lt;frac{14}{3})</span>.</p>\u0000</li>\u0000<li>\u0000<span>(3)</span>\u0000<p>The existence of a ground state solution for all <span>(c&gt;0)</span> when <span>(frac{14}{3}le q&lt;6)</span>.</p>\u0000</li>\u0000</ol><p> Furthermore, the paper presents the first non-existence result for the case <span>(mu le 0)</span> and <span>(2&lt;q&lt;6)</span>. In particular, refined estimates of energy levels are proposed, suggesting a new threshold of compactness in the <span>(L^2)</span>-constraint. This study addresses an open problem for <span>(2&lt;q&lt;frac{10}{3})</span> and fills a gap in the case <span>(frac{10}{3}le q&lt;frac{14}{3})</span>. We believe that our approach can be applied to a broader range of nonlinear terms with Sobolev critical growth, and the underlying ideas have potential for future development and applicability.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"158 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185191","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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