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Derivative of the Riemann–Hilbert map 黎曼-希尔伯特映射的导数
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-15 DOI: 10.1112/blms.70092
Vladimir Marković, Ognjen Tošić
{"title":"Derivative of the Riemann–Hilbert map","authors":"Vladimir Marković,&nbsp;Ognjen Tošić","doi":"10.1112/blms.70092","DOIUrl":"https://doi.org/10.1112/blms.70092","url":null,"abstract":"<p>Given a pair <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mo>∇</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(X,nabla)$</annotation>\u0000 </semantics></math>, consisting of a closed Riemann surface <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> and a holomorphic connection <span></span><math>\u0000 <semantics>\u0000 <mo>∇</mo>\u0000 <annotation>$nabla$</annotation>\u0000 </semantics></math> on the trivial principal bundle <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>×</mo>\u0000 <msub>\u0000 <mi>SL</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>C</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>→</mo>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <annotation>$Xtimes mathrm{SL}_2(mathbb {C})rightarrow X$</annotation>\u0000 </semantics></math>, the Riemann–Hilbert map sends <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mo>∇</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(X,nabla)$</annotation>\u0000 </semantics></math> to its monodromy representation. We compute the derivative of this map, and provide a simple description of the locus where it is injective, recovering in the process several previously obtained results.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2253-2264"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144814617","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 Calderón–Zygmund estimates for parabolic quasiminimizers 抛物型拟极值器的全局Calderón-Zygmund估计
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-14 DOI: 10.1112/blms.70094
Yumi Cho, Seungjin Ryu, Kyeong Song
{"title":"Global Calderón–Zygmund estimates for parabolic quasiminimizers","authors":"Yumi Cho,&nbsp;Seungjin Ryu,&nbsp;Kyeong Song","doi":"10.1112/blms.70094","DOIUrl":"https://doi.org/10.1112/blms.70094","url":null,"abstract":"<p>We prove global Calderón–Zygmund type estimates for parabolic quasiminimizers of integral functionals with <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-growth.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2265-2285"},"PeriodicalIF":0.9,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144814851","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
Generators of the preprojective CoHA of a quiver 颤振预投影余弦的产生器
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-14 DOI: 10.1112/blms.70093
Andrei Neguț
{"title":"Generators of the preprojective CoHA of a quiver","authors":"Andrei Neguț","doi":"10.1112/blms.70093","DOIUrl":"https://doi.org/10.1112/blms.70093","url":null,"abstract":"<p>In this short note, we refine a result of Schiffmann–Vasserot, by showing that the localized preprojective cohomological Hall algebra of any quiver is spherical, that is, generated by elements of minimal dimension.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2561-2570"},"PeriodicalIF":0.9,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815167","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
Qualitative properties of the heat content 热含量的定性性质
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-12 DOI: 10.1112/blms.70091
Michiel van den Berg, Katie Gittins
{"title":"Qualitative properties of the heat content","authors":"Michiel van den Berg,&nbsp;Katie Gittins","doi":"10.1112/blms.70091","DOIUrl":"https://doi.org/10.1112/blms.70091","url":null,"abstract":"<p>We obtain monotonicity and convexity results for the heat content of domains in Riemannian manifolds and in Euclidean space subject to various initial temperature conditions. We introduce the notion of a <i>strictly decreasing temperature set</i>, and show that it is a sufficient condition to ensure monotone heat content. In addition, in Euclidean space, we construct a domain and an initial condition for which the heat content is not monotone, as well as a domain and an initial condition for which the heat content is monotone but not convex.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2239-2252"},"PeriodicalIF":0.9,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70091","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144814921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the boundary criterion for relative cubulation: Multiended parabolics 关于相对计算的边界判据：多端抛物线
IF 0.8 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-08 DOI: 10.1112/blms.70087
Eduard Einstein, Suraj Krishna M S, Thomas Ng
{"title":"On the boundary criterion for relative cubulation: Multiended parabolics","authors":"Eduard Einstein,&nbsp;Suraj Krishna M S,&nbsp;Thomas Ng","doi":"10.1112/blms.70087","DOIUrl":"https://doi.org/10.1112/blms.70087","url":null,"abstract":"<p>In this note, we extend the boundary criterion for relative cubulation of the first author and Groves to the case when the peripheral subgroups are not necessarily one-ended. Specifically, if the boundary criterion is satisfied for a relatively hyperbolic group, we show that, up to taking a <i>refined peripheral structure</i>, the group admits a relatively geometric action on a CAT(0) cube complex. We anticipate that this refinement will be useful for constructing new relative cubulations in a variety of settings.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2177-2189"},"PeriodicalIF":0.8,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680994","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
Hilbert–Kunz multiplicity of powers of ideals in dimension two 二阶理想幂的Hilbert-Kunz多重性
IF 0.8 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-07 DOI: 10.1112/blms.70086
Alessandro De Stefani, Shreedevi K. Masuti, Maria Evelina Rossi, Jugal K. Verma
{"title":"Hilbert–Kunz multiplicity of powers of ideals in dimension two","authors":"Alessandro De Stefani,&nbsp;Shreedevi K. Masuti,&nbsp;Maria Evelina Rossi,&nbsp;Jugal K. Verma","doi":"10.1112/blms.70086","DOIUrl":"https://doi.org/10.1112/blms.70086","url":null,"abstract":"<p>We study the behavior of the Hilbert–Kunz multiplicity of powers of an ideal in a local ring. In dimension 2, we provide answers to some problems raised by Smirnov, and give a criterion to answer one of his questions in terms of a “Ratliff–Rush version” of the Hilbert–Kunz multiplicity.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2155-2176"},"PeriodicalIF":0.8,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70086","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Presentation of kernels of rational characters of right-angled Artin groups 直角Artin群的有理性质核的表示
IF 0.8 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-07 DOI: 10.1112/blms.70090
Montserrat Casals-Ruiz, Ilya Kazachkov, Mallika Roy
{"title":"Presentation of kernels of rational characters of right-angled Artin groups","authors":"Montserrat Casals-Ruiz,&nbsp;Ilya Kazachkov,&nbsp;Mallika Roy","doi":"10.1112/blms.70090","DOIUrl":"https://doi.org/10.1112/blms.70090","url":null,"abstract":"<p>In this note, we characterise when the kernel of a rational character of a right-angled Artin group, also known as generalised Bestiva–Brady group, is finitely generated and finitely presented. In these cases, we exhibit a finite generating set and a presentation. These results generalise Dicks and Leary's presentations of Bestiva–Brady kernels and provide an algebraic proof for the results proven by Meier, Meinert and VanWyk.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2219-2234"},"PeriodicalIF":0.8,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Double star arrangement and the pointed multinet 双星布局和点多网
IF 0.8 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-07 DOI: 10.1112/blms.70089
Yongqiang Liu, Wentao Xie
{"title":"Double star arrangement and the pointed multinet","authors":"Yongqiang Liu,&nbsp;Wentao Xie","doi":"10.1112/blms.70089","DOIUrl":"https://doi.org/10.1112/blms.70089","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$mathcal {A}$</annotation>\u0000 </semantics></math> be a hyperplane arrangement in a complex projective space. It is an open question if the degree one cohomology jump loci (with complex coefficients) are determined by the combinatorics of <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$mathcal {A}$</annotation>\u0000 </semantics></math>. By the work of Falk and Yuzvinsky [Compositio Math. 143 (2007), no. 4, 1069–1088] and Marco-Buzunáriz [Graphs Combin. 25 (2009), no. 4, 469–488], all the irreducible components passing through the origin are determined by the multinet structure, which is combinatorially determined. Denham and Suciu introduced the pointed multinet structure, which is combinatorially determined, to obtain examples of arrangements with translated positive-dimensional components in the degree one cohomology jump loci [Proc. Lond. Math. Soc. (3) 108 (2014), no. 6, 1435–1470]. Suciu asked the question if all translated positive-dimensional components appear in this manner [Ann. Fac. Sci. Toulouse Math. (6) 23 (2014), no. 2, 417–481]. In this paper, we show that the double star arrangement introduced by Ishibashi, Sugawara, and Yoshinaga [Adv. in Appl. Math. 162 (2025), Paper No. 102790, Example 3.2] gives a negative answer to this question.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2210-2218"},"PeriodicalIF":0.8,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681354","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
Étale motives of geometric origin Étale几何起源的动机
IF 0.8 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-07 DOI: 10.1112/blms.70085
Raphaël Ruimy, Swann Tubach
{"title":"Étale motives of geometric origin","authors":"Raphaël Ruimy,&nbsp;Swann Tubach","doi":"10.1112/blms.70085","DOIUrl":"https://doi.org/10.1112/blms.70085","url":null,"abstract":"<p>Over qcqs finite-dimensional schemes, we prove that étale motives of geometric origin can be characterised by a constructibility property which is purely categorical, giving a full answer to the question ‘Do all constructible étale motives come from geometry?’ which dates back to Cisinski and Déglise's work. We also show that they afford the continuity property and satisfy h-descent and Milnor excision.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2116-2131"},"PeriodicalIF":0.8,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70085","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Self-intersections of arcs on a pair of pants 一条裤子上的弧线的自交
IF 0.8 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-06 DOI: 10.1112/blms.70088
Nhat Minh Doan, Hanh Vo
{"title":"Self-intersections of arcs on a pair of pants","authors":"Nhat Minh Doan,&nbsp;Hanh Vo","doi":"10.1112/blms.70088","DOIUrl":"https://doi.org/10.1112/blms.70088","url":null,"abstract":"<p>We investigate arcs on a pair of pants and present an algorithm to compute the self-intersection number of an arc. Additionally, we establish bounds for the self-intersection number in terms of the word length. We also prove that the spectrum of self-intersection numbers of 2-low-lying arcs covers all natural numbers.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2190-2209"},"PeriodicalIF":0.8,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681287","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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