Mathematische Nachrichten最新文献

{"title":"On rank 3 instanton bundles on \u0000 \u0000 \u0000 P\u0000 3\u0000 \u0000 $mathbb {P}^3$","authors":"A. V. Andrade,&nbsp;D. R. Santiago,&nbsp;D. D. Silva,&nbsp;L. C. S. Sobral","doi":"10.1002/mana.202200332","DOIUrl":"10.1002/mana.202200332","url":null,"abstract":"<p>We investigate rank 3 instanton vector bundles on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$mathbb {P}^3$</annotation>\u0000 </semantics></math> of charge <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> and its correspondence with rational curves of degree <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$n+3$</annotation>\u0000 </semantics></math>. For <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$n=2$</annotation>\u0000 </semantics></math>, we present a correspondence between stable rank 3 instanton bundles and stable rank 2 reflexive linear sheaves of Chern classes <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>c</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>c</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>c</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>=</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>3</mn>\u0000 <mo>,</mo>\u0000 <mn>3</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$(c_1,c_2,c_3)=(-1,3,3)$</annotation>\u0000 </semantics></math> and we use this correspondence to compute the dimension of the family of stable rank 3 instanton bundles of charge 2. Finally, we use the results above to prove that the moduli space of rank 3 instanton bundles on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$mathbb {P}^3$</annotation>\u0000 </semantics></math> of charge 2 coincides with the moduli space of rank 3 stable locally free sheaves on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$mathbb {P}^3$</annotation>\u0000 </semantics></math> of Chern cla","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197815","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":"K3 surfaces with a symplectic automorphism of order 4","authors":"Benedetta Piroddi","doi":"10.1002/mana.202300052","DOIUrl":"10.1002/mana.202300052","url":null,"abstract":"<p>Given <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>, a K3 surface admitting a symplectic automorphism <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math> of order 4, we describe the isometry <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>τ</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$tau ^*$</annotation>\u0000 </semantics></math> on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mi>Z</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$H^2(X,mathbb {Z})$</annotation>\u0000 </semantics></math>. Having called <span></span><math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>Z</mi>\u0000 <mo>∼</mo>\u0000 </mover>\u0000 <annotation>$tilde{Z}$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>Y</mi>\u0000 <mo>∼</mo>\u0000 </mover>\u0000 <annotation>$tilde{Y}$</annotation>\u0000 </semantics></math>, respectively, the minimal resolutions of the quotient surfaces <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Z</mi>\u0000 <mo>=</mo>\u0000 <mi>X</mi>\u0000 <mo>/</mo>\u0000 <msup>\u0000 <mi>τ</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$Z=X/tau ^2$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Y</mi>\u0000 <mo>=</mo>\u0000 <mi>X</mi>\u0000 <mo>/</mo>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <annotation>$Y=X/tau$</annotation>\u0000 </semantics></math>, we also describe the maps induced in cohomology by the rational quotient maps <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>→</mo>\u0000 <mover>\u0000 <mi>Z</mi>\u0000 <mo>∼</mo>\u0000 </mover>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mi>X</mi>\u0000 <mo>→</mo>\u0000 <mover>\u0000 <mi>Y</mi>\u0000 <mo>∼</mo>\u0000 </mover>\u0000 </mrow>\u0000 <a","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140115230","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":"Normalized solutions to nonlinear Schrödinger equations with competing Hartree-type nonlinearities","authors":"Divyang Bhimani,&nbsp;Tianxiang Gou,&nbsp;Hichem Hajaiej","doi":"10.1002/mana.202200443","DOIUrl":"10.1002/mana.202200443","url":null,"abstract":"<p>In this paper, we consider solutions to the following nonlinear Schrödinger equation with competing Hartree-type nonlinearities,\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125377","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":"Effects of indirect signal absorption in the chemotaxis system involving singularly signal-dependent motilities","authors":"Yan Li,&nbsp;Jiaqi Wang,&nbsp;Fei Pan","doi":"10.1002/mana.202300182","DOIUrl":"10.1002/mana.202300182","url":null,"abstract":"<p>We consider the initial-boundary problem of the chemotaxis system with indirect consumption\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125396","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":"Convexity properties of Yoshikawa–Sparr interpolation spaces","authors":"Karol Aleksandrowicz,&nbsp;Stanisław Prus","doi":"10.1002/mana.202300388","DOIUrl":"10.1002/mana.202300388","url":null,"abstract":"<p>We study stability of the three geometric properties: uniform convexity, nearly uniform convexity, and property <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>β</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(beta)$</annotation>\u0000 </semantics></math> under the Yoshikawa–Sparr interpolation method when the resulting interpolation space is considered with various equivalent norms. We give an example which shows that interpolation spaces obtained by the discrete and continuous versions of the method need not be isometric and present a method of transferring geometric properties from the discrete case to the continuous one.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125183","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":"Complete real Kähler submanifolds","authors":"A. de Carvalho","doi":"10.1002/mana.202300369","DOIUrl":"10.1002/mana.202300369","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <msup>\u0000 <mi>M</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$f: M^{2n}rightarrow mathbb {R}^{2n+p}$</annotation>\u0000 </semantics></math> denote an isometric immersion of a Kähler manifold with complex dimension <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>≥</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$nge 2$</annotation>\u0000 </semantics></math> into Euclidean space with codimension <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>. We show that generic rank conditions on the second fundamental form of a non-minimal complete real Kähler submanifold <span></span><math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> imply that <span></span><math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> is a cylinder over a real Kähler submanifold <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mo>:</mo>\u0000 <msup>\u0000 <mi>N</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>p</mi>\u0000 <mo>+</mo>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$g: N^{2p}rightarrow mathbb {R}^{2p+p}$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140117548","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":"Ergodic properties of multiplication and weighted composition operators on spaces of holomorphic functions","authors":"Daniel Santacreu","doi":"10.1002/mana.202300430","DOIUrl":"10.1002/mana.202300430","url":null,"abstract":"<p>We obtain different results about the mean ergodicity of weighted composition operators when acting on the spaces <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 <mo>(</mo>\u0000 <mi>B</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$H(B)$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>H</mi>\u0000 <mi>b</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>B</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$H_b(B)$</annotation>\u0000 </semantics></math>, and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>B</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$H^infty (B)$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math> is the open unit ball of a Banach space, as well as about the compactness and the mean ergodicity of the multiplication operator. This study relates these properties of the operators with properties of the symbol and the weight defining such operators.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300430","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140115420","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":"On the completeness of root function system of the Dirac operator with two-point boundary conditions","authors":"Alexander Makin","doi":"10.1002/mana.202300241","DOIUrl":"10.1002/mana.202300241","url":null,"abstract":"<p>The paper is concerned with the completeness property of root functions of the Dirac operator with summable complex-valued potential and nonregular boundary conditions. We also obtain an explicit form for the fundamental solution system of the considered operator.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140046062","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":"On the structure of Nevanlinna measures","authors":"Mitja Nedic,&nbsp;Eero Saksman","doi":"10.1002/mana.202200135","DOIUrl":"10.1002/mana.202200135","url":null,"abstract":"<p>In this paper, we study the structural properties of Nevanlinna measures, that is, Borel measures that arise in the integral representation of Herglotz–Nevanlinna functions. In particular, we give a characterization of these measures in terms of their Fourier transform, characterize measures supported on hyperplanes including extremal measures, describe the structure of the singular part of the measures when some variable are set to a fixed value, and provide estimates for the measure of expanding and shrinking cubes. Corresponding results are stated also in the setting of the polydisc where applicable, and some of our proofs are actually performed via the polydisc.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202200135","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140034745","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":"Global existence for nonlocal quasilinear diffusion systems in nonisotropic nondivergence form","authors":"Catharine W. K. Lo,&nbsp;José Francisco Rodrigues","doi":"10.1002/mana.202200250","DOIUrl":"10.1002/mana.202200250","url":null,"abstract":"<p>We consider the quasilinear diffusion problem of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 <mo>=</mo>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>u</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <mtext>…</mtext>\u0000 <mo>,</mo>\u0000 <msup>\u0000 <mi>u</mi>\u0000 <mi>m</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$bm {u}=(u^1,ldots ,u^m)$</annotation>\u0000 </semantics></math>\u0000 \u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140034736","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}