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Hodge numbers of O’Grady 6 via Ngô strings 奥格雷迪的霍奇数 6 通过 Ngô 字符串
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-13 DOI: 10.1007/s00229-024-01540-8
Ben Wu
{"title":"Hodge numbers of O’Grady 6 via Ngô strings","authors":"Ben Wu","doi":"10.1007/s00229-024-01540-8","DOIUrl":"https://doi.org/10.1007/s00229-024-01540-8","url":null,"abstract":"<p>We give an alternative computation of the Betti and Hodge numbers for manifolds of <i>OG</i>6 type using the method of Ngô Strings introduced by de Cataldo, Rapagnetta, and Saccà.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"148 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Poisson commutative subalgebras associated with a Cartan subalgebra 与 Cartan 子代数相关的泊松交换子代数
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-13 DOI: 10.1007/s00229-024-01545-3
Oksana S. Yakimova
{"title":"Poisson commutative subalgebras associated with a Cartan subalgebra","authors":"Oksana S. Yakimova","doi":"10.1007/s00229-024-01545-3","DOIUrl":"https://doi.org/10.1007/s00229-024-01545-3","url":null,"abstract":"<p>Let <span>({mathfrak g})</span> be a reductive Lie algebra and <span>(mathfrak tsubset mathfrak g)</span> a Cartan subalgebra. The <span>(mathfrak t)</span>-stable decomposition <span>({mathfrak g}=mathfrak toplus {mathfrak m})</span> yields a bi-grading of the symmetric algebra <span>({mathcal {S}}({mathfrak g}))</span>. The subalgebra <span>({mathcal {Z}}_{({mathfrak g},mathfrak t)})</span> generated by the bi-homogenous components of the symmetric invariants <span>(Fin {mathcal {S}}({mathfrak g})^{mathfrak g})</span> is known to be Poisson commutative. Furthermore the algebra <span>({tilde{{mathcal {Z}}}}=textsf{alg}langle {mathcal {Z}}_{({mathfrak g},{mathfrak t})},{mathfrak t}rangle )</span> is also Poisson commutative. We investigate relations between <span>({tilde{{mathcal {Z}}}})</span> and Mishchenko–Fomenko subalgebras. In type <span>A</span>, we construct a quantisation of <span>({tilde{{mathcal {Z}}}})</span> making use of quantum Mishchenko–Fomenko algebras.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"2013 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Weights for compact connected Lie groups 紧凑相连李群的权重
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-09 DOI: 10.1007/s00229-024-01538-2
Radha Kessar, Gunter Malle, Jason Semeraro
{"title":"Weights for compact connected Lie groups","authors":"Radha Kessar, Gunter Malle, Jason Semeraro","doi":"10.1007/s00229-024-01538-2","DOIUrl":"https://doi.org/10.1007/s00229-024-01538-2","url":null,"abstract":"<p>Let <span>(ell )</span> be a prime. If <span>(textbf{G})</span> is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from <span>(ell )</span>, and <span>(ell )</span> is a good prime for <span>(textbf{G})</span>, we show that the number of weights of the <span>(ell )</span>-fusion system of <span>(textbf{G})</span> is equal to the number of irreducible characters of its Weyl group. The proof relies on the classification of <span>(ell )</span>-stubborn subgroups in compact Lie groups.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"57 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140105436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Upper bounds for the critical values of homology classes of loops 循环同构类临界值的上限
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-02 DOI: 10.1007/s00229-024-01541-7
Hans-Bert Rademacher
{"title":"Upper bounds for the critical values of homology classes of loops","authors":"Hans-Bert Rademacher","doi":"10.1007/s00229-024-01541-7","DOIUrl":"https://doi.org/10.1007/s00229-024-01541-7","url":null,"abstract":"<p>In this short note we discuss upper bounds for the critical values of homology classes in the based and free loop space of compact manifolds carrying a Riemannian or Finsler metric of positive Ricci curvature. In particular it follows that a shortest closed geodesic on a compact and simply-connected <i>n</i>-dimensional manifold of positive Ricci curvature <span>(text {Ric}ge n-1)</span> has length <span>(le n pi .)</span> This improves the bound <span>(8pi (n-1))</span> given by Rotman (Positive Ricci curvature and the length of a shortest periodic geodesic. arXiv:2203.09492, 2022).</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"2 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140018846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Diameter estimates for surfaces in conformally flat spaces 共形平面空间中曲面的直径估计值
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-01 DOI: 10.1007/s00229-024-01539-1
Marco Flaim, Christian Scharrer
{"title":"Diameter estimates for surfaces in conformally flat spaces","authors":"Marco Flaim, Christian Scharrer","doi":"10.1007/s00229-024-01539-1","DOIUrl":"https://doi.org/10.1007/s00229-024-01539-1","url":null,"abstract":"<p>The aim of this paper is to give an upper bound for the intrinsic diameter of a surface with boundary immersed in a conformally flat three dimensional Riemannian manifold in terms of the integral of the mean curvature and of the length of its boundary. Of particular interest is the application of the inequality to minimal surfaces in the three-sphere and in the hyperbolic space. Here the result implies an a priori estimate for connected solutions of Plateau’s problem, as well as a necessary condition on the boundary data for the existence of such solutions. The proof follows a construction of Miura and uses a diameter bound for closed surfaces obtained by Topping and Wu–Zheng.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"18 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140018869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Sign-changing solution for logarithmic elliptic equations with critical exponent 有临界指数的对数椭圆方程的符号变化解法
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-01 DOI: 10.1007/s00229-024-01535-5
Tianhao Liu, Wenming Zou
{"title":"Sign-changing solution for logarithmic elliptic equations with critical exponent","authors":"Tianhao Liu, Wenming Zou","doi":"10.1007/s00229-024-01535-5","DOIUrl":"https://doi.org/10.1007/s00229-024-01535-5","url":null,"abstract":"<p>In this paper, we consider the logarithmic elliptic equations with critical exponent </p><span>$$begin{aligned} left{ begin{array}{ll} -Delta u=lambda u+ |u|^{2^*-2}u+theta ulog u^2, u in H_0^1(Omega ), quad Omega subset {{mathbb {R}}}^N. end{array}right. end{aligned}$$</span><p>Here, the parameters <span>(Nge 6)</span>, <span>(lambda in {{mathbb {R}}})</span>, <span>(theta &gt;0)</span> and <span>( 2^*=frac{2N}{N-2} )</span> is the Sobolev critical exponent. We prove the existence of a sign-changing solution with exactly two nodal domain for an arbitrary smooth bounded domain <span>(Omega subset {mathbb {R}}^{N})</span>. When <span>(Omega =B_R(0))</span> is a ball, we also construct infinitely many radial sign-changing solutions with alternating signs and prescribed nodal characteristic.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"22 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Singular Yamabe problem for scalar flat metrics on the sphere 球面上标量平面度量的山边奇异问题
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-24 DOI: 10.1007/s00229-023-01527-x
Aram L. Karakhanyan
{"title":"Singular Yamabe problem for scalar flat metrics on the sphere","authors":"Aram L. Karakhanyan","doi":"10.1007/s00229-023-01527-x","DOIUrl":"https://doi.org/10.1007/s00229-023-01527-x","url":null,"abstract":"<p>Let <span>(Omega )</span> be a domain on the unit <i>n</i>-sphere <span>( {mathbb {S}}^n)</span> and <span>( overset{{,}_circ }{g})</span> the standard metric of <span>({mathbb {S}}^n)</span>, <span>(nge 3)</span>. We show that there exists a conformal metric <i>g</i> with vanishing scalar curvature <span>(R(g)=0)</span> such that <span>((Omega , g))</span> is complete if and only if the Bessel capacity <span>({mathcal {C}}_{alpha , q}({mathbb {S}}^nsetminus Omega )=0)</span>, where <span>(alpha =1+frac{2}{n})</span> and <span>(q=frac{n}{2})</span>. Our analysis utilizes some well known properties of capacity and Wolff potentials, as well as a version of the Hopf–Rinow theorem for the divergent curves.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"166 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139579627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Chern number inequalities of deformed Hermitian-Yang-Mills metrics on four dimensional Kähler manifolds 四维凯勒流形上变形赫米蒂-杨-米尔斯度量的切尔数不等式
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-21 DOI: 10.1007/s00229-023-01531-1
Xiaoli Han, Xishen Jin
{"title":"Chern number inequalities of deformed Hermitian-Yang-Mills metrics on four dimensional Kähler manifolds","authors":"Xiaoli Han, Xishen Jin","doi":"10.1007/s00229-023-01531-1","DOIUrl":"https://doi.org/10.1007/s00229-023-01531-1","url":null,"abstract":"<p>In this paper, we give an affirmative answer to a conjecture of Collins-Yau [8]. We investigate the Chern number inequalities on 4-dimensional Kähler manifolds admitting the deformed Hermitian-Yang-Mills metrics under the assumption <span>({{hat{theta }}}in (pi ,2pi ))</span>.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"5 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139508979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The string topology coproduct on complex and quaternionic projective space 复投影空间和四元投影空间上的弦拓扑共积
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-18 DOI: 10.1007/s00229-023-01532-0
Maximilian Stegemeyer
{"title":"The string topology coproduct on complex and quaternionic projective space","authors":"Maximilian Stegemeyer","doi":"10.1007/s00229-023-01532-0","DOIUrl":"https://doi.org/10.1007/s00229-023-01532-0","url":null,"abstract":"<p>On the free loop space of compact symmetric spaces Ziller introduced explicit cycles generating the homology of the free loop space. We use these explicit cycles to compute the string topology coproduct on complex and quaternionic projective space. The behavior of the Goresky-Hingston product for these spaces then follows directly.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"59 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139496220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Mass-growth of triangulated auto-equivalences 三角形自等式的质量增长
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-18 DOI: 10.1007/s00229-023-01533-z
Jon Woolf
{"title":"Mass-growth of triangulated auto-equivalences","authors":"Jon Woolf","doi":"10.1007/s00229-023-01533-z","DOIUrl":"https://doi.org/10.1007/s00229-023-01533-z","url":null,"abstract":"<p>We relate the mass growth (with respect to a stability condition) of an exact auto-equivalence of a triangulated category to the dynamical behaviour of its action on the space of stability conditions. One consequence is that this action is free and proper whenever the mass growth is non-vanishing.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"30 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139496216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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