Journal of the London Mathematical Society-Second Series最新文献

{"title":"Algebraic fibre spaces with strictly nef relative anti-log canonical divisor","authors":"Jie Liu,&nbsp;Wenhao Ou,&nbsp;Juanyong Wang,&nbsp;Xiaokui Yang,&nbsp;Guolei Zhong","doi":"10.1112/jlms.12942","DOIUrl":"https://doi.org/10.1112/jlms.12942","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mi>Δ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(X,varDelta)$</annotation>\u0000 </semantics></math> be a projective klt pair, and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <mi>X</mi>\u0000 <mo>→</mo>\u0000 <mi>Y</mi>\u0000 </mrow>\u0000 <annotation>$fcolon Xrightarrow Y$</annotation>\u0000 </semantics></math> a fibration to a smooth projective variety <span></span><math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$Y$</annotation>\u0000 </semantics></math> with strictly nef relative anti-log canonical divisor <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>/</mo>\u0000 <mi>Y</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <mi>Δ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$-(K_{X/Y}+varDelta)$</annotation>\u0000 </semantics></math>. We prove that <span></span><math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> is a locally trivial fibration with rationally connected fibres, and the base <span></span><math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$Y$</annotation>\u0000 </semantics></math> is a canonically polarized hyperbolic manifold. In particular, when <span></span><math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$Y$</annotation>\u0000 </semantics></math> is a single point, we establish that <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> is rationally connected. Moreover, when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>dim</mo>\u0000 <mi>X</mi>\u0000 <mo>=</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$dim X=3$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mi>X</mi>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <mi>Δ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$-(K_X","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141182262","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}

{"title":"Branching random walk with non-local competition","authors":"Pascal Maillard,&nbsp;Sarah Penington","doi":"10.1112/jlms.12919","DOIUrl":"https://doi.org/10.1112/jlms.12919","url":null,"abstract":"<p>We study the Bolker–Pacala–Dieckmann–Law (BPDL) model of population dynamics in the regime of large population density. The BPDL model is a particle system in which particles reproduce, move randomly in space and compete with each other locally. We rigorously prove global survival as well as a shape theorem describing the asymptotic spread of the population, when the population density is sufficiently large. In contrast to most previous studies, we allow the competition kernel to have an arbitrary, even infinite range, whence the term <i>non-local competition</i>. This makes the particle system non-monotone and of infinite-range dependence, meaning that the usual comparison arguments break down and have to be replaced by a more hands-on approach. Some ideas in the proof are inspired by works on the non-local Fisher-KPP equation, but the stochasticity of the model creates new difficulties.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12919","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141164788","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}

{"title":"Quadratic forms and Genus Theory: A link with 2-descent and an application to nontrivial specializations of ideal classes","authors":"William Dallaporta","doi":"10.1112/jlms.12921","DOIUrl":"https://doi.org/10.1112/jlms.12921","url":null,"abstract":"<p>Genus Theory is a classical feature of integral binary quadratic forms. Using the author's generalization of the well-known correspondence between quadratic form classes and ideal classes of quadratic algebras, we extend it to the case when quadratic forms are twisted and have coefficients in any principal ideal domain (PID) <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math>. When <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mo>=</mo>\u0000 <mi>K</mi>\u0000 <mo>[</mo>\u0000 <mi>X</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>${R = mathbb {K}[X]}$</annotation>\u0000 </semantics></math>, we show that the Genus Theory map is the quadratic form version of the 2-descent map on a certain hyperelliptic curve. As an application, we make a contribution to a question of Agboola and Pappas regarding a specialization problem of divisor classes on hyperelliptic curves. Under suitable assumptions, we prove that the set of nontrivial specializations has density 1.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12921","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141165032","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}

{"title":"Topological endomorphism rings of tilting complexes","authors":"Michal Hrbek","doi":"10.1112/jlms.12939","DOIUrl":"https://doi.org/10.1112/jlms.12939","url":null,"abstract":"<p>In a compactly generated triangulated category, we introduce a class of tilting objects satisfying a certain purity condition. We call these the decent tilting objects and show that the tilting heart induced by any such object is equivalent to a category of contramodules over the endomorphism ring of the tilting object endowed with a natural linear topology. This extends the recent result for <i>n</i>-tilting modules by Positselski and Št'ovíček. In the setting of the derived category of modules over a ring, we show that the decent tilting complexes are precisely the silting complexes such that their character dual is cotilting. The hearts of cotilting complexes of cofinite type turn out to be equivalent to the category of discrete modules with respect to the same topological ring. Finally, we provide a kind of Morita theory in this setting: Decent tilting complexes correspond to pairs consisting of a tilting and a cotilting-derived equivalence as described above tied together by a tensor compatibility condition.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12939","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141165015","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}

{"title":"Parafree graphs of groups with cyclic edge groups","authors":"Andrei Jaikin-Zapirain,&nbsp;Ismael Morales","doi":"10.1112/jlms.12937","DOIUrl":"https://doi.org/10.1112/jlms.12937","url":null,"abstract":"<p>We establish a combination theorem for parafree groups. These groups were introduced by Baumslag in the sixties. One of the current motivations for a better understanding of their structure is that they show up naturally in connection with Remeslennikov's conjecture on the profinite rigidity of free groups. In this article, we determine when the fundamental group of a finite graph of groups with cyclic edge groups is parafree.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12937","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141097921","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}

{"title":"Blocking sets, minimal codes and trifferent codes","authors":"Anurag Bishnoi,&nbsp;Jozefien D'haeseleer,&nbsp;Dion Gijswijt,&nbsp;Aditya Potukuchi","doi":"10.1112/jlms.12938","DOIUrl":"https://doi.org/10.1112/jlms.12938","url":null,"abstract":"<p>We prove new upper bounds on the smallest size of affine blocking sets, that is, sets of points in a finite affine space that intersect every affine subspace of a fixed codimension. We show an equivalence between affine blocking sets with respect to codimension-2 subspaces that are generated by taking a union of lines through the origin, and strong blocking sets in the corresponding projective space, which in turn are equivalent to minimal codes. Using this equivalence, we improve the current best upper bounds on the smallest size of a strong blocking set in finite projective spaces over fields of size at least 3. Furthermore, using coding theoretic techniques, we improve the current best lower bounds on a strong blocking set. Our main motivation for these new bounds is their application to trifferent codes, which are sets of ternary codes of length <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> with the property that for any three distinct codewords there is a coordinate where they all have distinct values. Over the finite field <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <annotation>$mathbb {F}_3$</annotation>\u0000 </semantics></math>, we prove that minimal codes are equivalent to linear trifferent codes. Using this equivalence, we show that any linear trifferent code of length <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> has size at most <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mn>3</mn>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>/</mo>\u0000 <mn>4.55</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$3^{n/4.55}$</annotation>\u0000 </semantics></math>, improving the recent upper bound of Pohoata and Zakharov. Moreover, we show the existence of linear trifferent codes of length <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> and size at least <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mfrac>\u0000 <mn>1</mn>\u0000 <mn>3</mn>\u0000 </mfrac>\u0000 <msup>\u0000 <mfenced>\u0000 <mn>9</mn>\u0000 <mo>/</mo>\u0000 <mn>5</mn>\u0000 </mfenced>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>/</mo>\u0000 <mn>4</mn>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12938","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141156523","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}

{"title":"Completely bounded norms of \u0000 \u0000 k\u0000 $k$\u0000 -positive maps","authors":"Guillaume Aubrun,&nbsp;Kenneth R. Davidson,&nbsp;Alexander Müller-Hermes,&nbsp;Vern I. Paulsen,&nbsp;Mizanur Rahaman","doi":"10.1112/jlms.12936","DOIUrl":"https://doi.org/10.1112/jlms.12936","url":null,"abstract":"<p>Given an operator system <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$mathcal {S}$</annotation>\u0000 </semantics></math>, we define the parameters <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>r</mi>\u0000 <mi>k</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>S</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$r_k(mathcal {S})$</annotation>\u0000 </semantics></math> (resp. <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>d</mi>\u0000 <mi>k</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>S</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$d_k(mathcal {S})$</annotation>\u0000 </semantics></math>) defined as the maximal value of the completely bounded norm of a unital <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>-positive map from an arbitrary operator system into <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$mathcal {S}$</annotation>\u0000 </semantics></math> (resp. from <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$mathcal {S}$</annotation>\u0000 </semantics></math> into an arbitrary operator system). In the case of the matrix algebras <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$mathsf {M}_n$</annotation>\u0000 </semantics></math>, for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>⩽</mo>\u0000 <mi>k</mi>\u0000 <mo>⩽</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$1 leqslant k leqslant n$</annotation>\u0000 </semantics></math>, we compute the exact value <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>r</mi>\u0000 <mi>k</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>=</mo>\u0000 <mfrac>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141097920","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}

{"title":"Iwahori-metaplectic duality","authors":"Ben Brubaker,&nbsp;Valentin Buciumas,&nbsp;Daniel Bump,&nbsp;Henrik P. A. Gustafsson","doi":"10.1112/jlms.12896","DOIUrl":"https://doi.org/10.1112/jlms.12896","url":null,"abstract":"<p>We construct a family of solvable lattice models whose partition functions include <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-adic Whittaker functions for general linear groups from two very different sources: from Iwahori-fixed vectors and from metaplectic covers. Interpolating between them by Drinfeld twisting, we uncover unexpected relationships between Iwahori and metaplectic Whittaker functions. This leads to new Demazure operator recurrence relations for spherical metaplectic Whittaker functions. In prior work of the authors it was shown that the row transfer matrices of certain lattice models for spherical metaplectic Whittaker functions could be represented as ‘half-vertex operators’ operating on the <span></span><math>\u0000 <semantics>\u0000 <mi>q</mi>\u0000 <annotation>$q$</annotation>\u0000 </semantics></math>-Fock space of Kashiwara, Miwa and Stern. In this paper the same is shown for all the members of this more general family of lattice models including the one representing Iwahori Whittaker functions.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12896","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141085086","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}

{"title":"Rational cross-sections, bounded generation, and orders on groups","authors":"Corentin Bodart","doi":"10.1112/jlms.12920","DOIUrl":"https://doi.org/10.1112/jlms.12920","url":null,"abstract":"<p>We provide new examples of groups without rational cross-sections (also called regular normal forms), using connections with bounded generation and rational orders on groups. Our examples contain a finitely presented HNN-extension of the first Grigorchuk group. This last group is the first example of finitely presented group with solvable word problem and without rational cross-sections. It is also not autostackable, and has no left-regular complete rewriting system.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12920","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141085084","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}

{"title":"Valuations, completions, and hyperbolic actions of metabelian groups","authors":"Carolyn R. Abbott,&nbsp;Sahana Balasubramanya,&nbsp;Alexander J. Rasmussen","doi":"10.1112/jlms.12916","DOIUrl":"https://doi.org/10.1112/jlms.12916","url":null,"abstract":"<p>Actions on hyperbolic metric spaces are an important tool for studying groups, and so it is natural, but difficult, to attempt to classify all such actions of a fixed group. In this paper, we build strong connections between hyperbolic geometry and commutative algebra in order to classify the cobounded hyperbolic actions of numerous metabelian groups up to a coarse equivalence. In particular, we turn this classification problem into the problems of classifying ideals in the completions of certain rings and calculating invariant subspaces of matrices. We use this framework to classify the cobounded hyperbolic actions of many abelian-by-cyclic groups associated to expanding integer matrices. Each such action is equivalent to an action on a tree or on a Heintze group (a classically studied class of negatively curved Lie groups). Our investigations incorporate number systems, factorization in formal power series rings, completions, and valuations.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12916","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141085085","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}