{"title":"Arithmetic progressions and holomorphic phase retrieval","authors":"Lukas Liehr","doi":"10.1112/blms.13134","DOIUrl":"https://doi.org/10.1112/blms.13134","url":null,"abstract":"<p>We study the determination of a holomorphic function from its absolute value. Given a parameter <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>θ</mi>\u0000 <mo>∈</mo>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$theta in mathbb {R}$</annotation>\u0000 </semantics></math>, we derive the following characterization of uniqueness in terms of rigidity of a set <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Λ</mi>\u0000 <mo>⊆</mo>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$Lambda subseteq mathbb {R}$</annotation>\u0000 </semantics></math>: if <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathcal {F}$</annotation>\u0000 </semantics></math> is a vector space of entire functions containing all exponentials <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>e</mi>\u0000 <mrow>\u0000 <mi>ξ</mi>\u0000 <mi>z</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mi>ξ</mi>\u0000 <mo>∈</mo>\u0000 <mi>C</mi>\u0000 <mo>∖</mo>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <mn>0</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$e^{xi z}, , xi in mathbb {C} setminus lbrace 0 rbrace$</annotation>\u0000 </semantics></math>, then every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <mo>∈</mo>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 <annotation>$F in mathcal {F}$</annotation>\u0000 </semantics></math> is uniquely determined up to a unimodular phase factor by <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <mo>|</mo>\u0000 <mi>F</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>z</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>|</mo>\u0000 <mo>:</mo>\u0000 <mi>z</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>e</mi>\u0000 <mrow>\u0000 <mi>i</mi>\u0000 <mi>θ</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>R</mi>\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 11","pages":"3316-3330"},"PeriodicalIF":0.8,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13134","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573861","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}
{"title":"Autoequivalences of blow-ups of minimal surfaces","authors":"Xianyu Hu, Johannes Krah","doi":"10.1112/blms.13131","DOIUrl":"https://doi.org/10.1112/blms.13131","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> be the blow-up of <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>P</mi>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msubsup>\u0000 <annotation>$mathbb {P}^2_mathbb {C}$</annotation>\u0000 </semantics></math> in a finite set of very general points. We deduce from the work of Uehara [Trans. Amer. Math. Soc. <b>371</b> (2019), no. 5, 3529–3547] that <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> has only standard autoequivalences, no non-trivial Fourier–Mukai partners, and admits no spherical objects. If <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> is the blow-up of <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>P</mi>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msubsup>\u0000 <annotation>$mathbb {P}^2_mathbb {C}$</annotation>\u0000 </semantics></math> in 9 very general points, we provide an alternate and direct proof of the corresponding statement. Further, we show that the same result holds if <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> is a blow-up of finitely many points in a minimal surface of non-negative Kodaira dimension which contains no <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(-2)$</annotation>\u0000 </semantics></math>-curves. Independently, we characterize spherical objects on blow-ups of minimal surfaces of positive Kodaira dimension.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 10","pages":"3257-3267"},"PeriodicalIF":0.8,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13131","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142435224","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}
{"title":"Galois invariants of finite abelian descent and Brauer sets","authors":"Brendan Creutz, Jesse Pajwani, José Felipe Voloch","doi":"10.1112/blms.13130","DOIUrl":"https://doi.org/10.1112/blms.13130","url":null,"abstract":"<p>For a variety over a global field, one can consider subsets of the set of adelic points of the variety cut out by finite abelian descent or Brauer–Manin obstructions. Given a Galois extension of the ground field, one can consider similar sets over the extension and take Galois invariants. In this paper, we study under which circumstances the Galois invariants recover the obstruction sets over the ground field. As an application of our results, we study finite abelian descent and Brauer–Manin obstructions for isotrivial curves over function fields and extend results obtained by the first and last authors for constant curves to the isotrivial case.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 10","pages":"3240-3256"},"PeriodicalIF":0.8,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13130","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142435123","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}
{"title":"Local mirror symmetry via SYZ","authors":"Benjamin Gammage","doi":"10.1112/blms.13126","DOIUrl":"https://doi.org/10.1112/blms.13126","url":null,"abstract":"<p>In this note, we explain how mirror symmetry for basic local models in the Gross–Siebert program can be understood through the nontoric blowup construction described by Gross–Hacking–Keel. This is part of a program to understand the symplectic geometry of affine cluster varieties through their SYZ fibrations.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 10","pages":"3181-3195"},"PeriodicalIF":0.8,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142435066","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}
{"title":"The inertia bound is far from tight","authors":"Matthew Kwan, Yuval Wigderson","doi":"10.1112/blms.13127","DOIUrl":"https://doi.org/10.1112/blms.13127","url":null,"abstract":"<p>The inertia bound and ratio bound (also known as the Cvetković bound and Hoffman bound) are two fundamental inequalities in spectral graph theory, giving upper bounds on the independence number <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>(</mo>\u0000 <mi>G</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$alpha (G)$</annotation>\u0000 </semantics></math> of a graph <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> in terms of spectral information about a weighted adjacency matrix of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>. For both inequalities, given a graph <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>, one needs to make a judicious choice of weighted adjacency matrix to obtain as strong a bound as possible. While there is a well-established theory surrounding the ratio bound, the inertia bound is much more mysterious, and its limits are rather unclear. In fact, only recently did Sinkovic find the first example of a graph for which the inertia bound is not tight (for any weighted adjacency matrix), answering a longstanding question of Godsil. We show that the inertia bound can be extremely far from tight, and in fact can significantly underperform the ratio bound: for example, one of our results is that for infinitely many <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>, there is an <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-vertex graph for which even the unweighted ratio bound can prove <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>G</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>⩽</mo>\u0000 <mn>4</mn>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 <mo>/</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$alpha (G)leqslant 4n^{3/4}$</annotation>\u0000 </semantics></math>, but the inertia bound is always at least <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 10","pages":"3196-3208"},"PeriodicalIF":0.8,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13127","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142435806","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}
{"title":"Unstability problem of real analytic maps","authors":"Karim Bekka, Satoshi Koike, Toru Ohmoto, Masahiro Shiota, Masato Tanabe","doi":"10.1112/blms.13124","DOIUrl":"https://doi.org/10.1112/blms.13124","url":null,"abstract":"<p>As well known, the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$C^infty$</annotation>\u0000 </semantics></math> stability of proper <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$C^infty$</annotation>\u0000 </semantics></math> maps is characterized by the infinitesimal <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$C^infty$</annotation>\u0000 </semantics></math> stability. In the present paper, we study the counterpart in real analytic context. In particular, we show that the infinitesimal <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>ω</mi>\u0000 </msup>\u0000 <annotation>$C^omega$</annotation>\u0000 </semantics></math> stability does not imply <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>ω</mi>\u0000 </msup>\u0000 <annotation>$C^omega$</annotation>\u0000 </semantics></math> stability; for instance, <i>a Whitney umbrella</i> <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {R}^2 rightarrow mathbb {R}^3$</annotation>\u0000 </semantics></math> <i>is not</i> <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>ω</mi>\u0000 </msup>\u0000 <annotation>$C^omega$</annotation>\u0000 </semantics></math> <i>stable</i>. A main tool for the proof is a relative version of Whitney's analytic approximation theorem that is shown by using H. Cartan's Theorems A and B.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 10","pages":"3174-3180"},"PeriodicalIF":0.8,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142435819","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}
{"title":"Solubility of additive forms of twice odd degree over totally ramified extensions of \u0000 \u0000 \u0000 Q\u0000 2\u0000 \u0000 $mathbb {Q}_2$","authors":"Drew Duncan","doi":"10.1112/blms.13120","DOIUrl":"10.1112/blms.13120","url":null,"abstract":"<p>We prove that an additive form of degree <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation>$d=2m$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math> odd over any totally ramified extension of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Q</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$mathbb {Q}_2$</annotation>\u0000 </semantics></math> has a nontrivial zero if the number of variables <span></span><math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>$s$</annotation>\u0000 </semantics></math> satisfies <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 <mo>⩾</mo>\u0000 <mfrac>\u0000 <msup>\u0000 <mi>d</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mn>4</mn>\u0000 </mfrac>\u0000 <mo>+</mo>\u0000 <mn>3</mn>\u0000 <mi>d</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$s geqslant frac{d^2}{4} + 3d + 1$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 10","pages":"3129-3133"},"PeriodicalIF":0.8,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141814035","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}
Leif Döring, Mladen Savov, Lukas Trottner, Alexander R. Watson
{"title":"The uniqueness of the Wiener–Hopf factorisation of Lévy processes and random walks","authors":"Leif Döring, Mladen Savov, Lukas Trottner, Alexander R. Watson","doi":"10.1112/blms.13112","DOIUrl":"https://doi.org/10.1112/blms.13112","url":null,"abstract":"<p>We prove that the spatial Wiener–Hopf factorisation of a Lévy process or random walk without killing is unique.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 9","pages":"2951-2968"},"PeriodicalIF":0.8,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13112","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142165641","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}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
