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Newton strata in Levi subgroups 列维分组中的牛顿层
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-04 DOI: 10.1007/s00229-024-01566-y
Felix Schremmer
{"title":"Newton strata in Levi subgroups","authors":"Felix Schremmer","doi":"10.1007/s00229-024-01566-y","DOIUrl":"https://doi.org/10.1007/s00229-024-01566-y","url":null,"abstract":"<p>Certain Iwahori double cosets in the loop group of a reductive group, known under the names of <i>P</i>-alcoves or <span>((J,w,delta ))</span>-alcoves, play an important role in the study of affine Deligne–Lusztig varieties. For such an Iwahori double coset, its Newton stratification is related to the Newton stratification of an Iwahori double coset in a Levi subgroup. We study this relationship further, providing in particular a bijection between the occurring Newton strata. As an application, we prove a conjecture of Dong-Gyu Lim, giving a non-emptiness criterion for basic affine Deligne–Lusztig varieties.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"6 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255173","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
A note about the generic irreducibility of the spectrum of the Laplacian on homogeneous spaces 关于同质空间上拉普拉斯频谱一般不可还原性的说明
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-03 DOI: 10.1007/s00229-024-01567-x
Diego S. de Oliveira, Marcus A. M. Marrocos
{"title":"A note about the generic irreducibility of the spectrum of the Laplacian on homogeneous spaces","authors":"Diego S. de Oliveira, Marcus A. M. Marrocos","doi":"10.1007/s00229-024-01567-x","DOIUrl":"https://doi.org/10.1007/s00229-024-01567-x","url":null,"abstract":"<p>Petrecca and Röser (Mathematische Zeitschrift 291:395–419, 2018) and Schueth (Ann Global Anal Geom 52:187–200, 2017) had shown that for a generic <i>G</i>-invariant metric <i>g</i> on certain compact homogeneous spaces <span>(M=G/K)</span> (including symmetric spaces of rank 1 and some Lie groups), the spectrum of the Laplace-Beltrami operator <span>(Delta _g)</span> was real <i>G</i>-simple. The same is not true for the complex version of <span>(Delta _g)</span> when there is a presence of representations of complex or quaternionic type. We show that these types of representations induces a <span>(Q_8)</span>-action that commutes with the Laplacian in such way that <i>G</i>-properties of the real version of the operator have to be understood as <span>((Q_8 times G))</span>-properties on its corresponding complex version.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"101 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255580","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
W-triviality of low dimensional manifolds 低维流形的 W 三维性
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-03 DOI: 10.1007/s00229-024-01575-x
Aritra C. Bhattacharya, Bikramjit Kundu, Aniruddha C. Naolekar
{"title":"W-triviality of low dimensional manifolds","authors":"Aritra C. Bhattacharya, Bikramjit Kundu, Aniruddha C. Naolekar","doi":"10.1007/s00229-024-01575-x","DOIUrl":"https://doi.org/10.1007/s00229-024-01575-x","url":null,"abstract":"<p>A space <i>X</i> is <i>W</i>-trivial if for every real vector bundle <span>(alpha )</span> over <i>X</i> the total Stiefel-Whitney class <span>(w(alpha ))</span> is 1. It follows from a result of Milnor that if <i>X</i> is an orientable closed smooth manifold of dimension 1, 2, 4 or 8, then <i>X</i> is not <i>W</i>-trivial. In this note we completely characterize <i>W</i>-trivial orientable connected closed smooth manifolds in dimensions 3, 5 and 6. In dimension 7, we describe necessary conditions for an orientable connected closed smooth 7-manifold to be <i>W</i>-trivial.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"66 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255171","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
A rigidity theorem for self-expanders 自展开式的刚性定理
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-03 DOI: 10.1007/s00229-024-01573-z
Zhi Li, Guoxin Wei
{"title":"A rigidity theorem for self-expanders","authors":"Zhi Li, Guoxin Wei","doi":"10.1007/s00229-024-01573-z","DOIUrl":"https://doi.org/10.1007/s00229-024-01573-z","url":null,"abstract":"<p>In this paper, we completely classify 3-dimensional complete self-expanders with constant squared norm <i>S</i> of the second fundamental form and constant <span>(f_{3})</span> in the Euclidean space <span>({mathbb {R}}^{4})</span>, where <span>(h_{ij})</span> are components of the second fundamental form, <span>(S=sum _{i,j}h^{2}_{ij})</span> and <span>(f_{3}=sum _{i,j,k}h_{ij}h_{jk}h_{ki})</span>.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"112 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255175","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
Archimedean distinguished representations and exceptional poles 阿基米德区分表示和特殊极点
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-01 DOI: 10.1007/s00229-024-01568-w
Akash Yadav
{"title":"Archimedean distinguished representations and exceptional poles","authors":"Akash Yadav","doi":"10.1007/s00229-024-01568-w","DOIUrl":"https://doi.org/10.1007/s00229-024-01568-w","url":null,"abstract":"<p>Let <i>F</i> be an archimedean local field and let <i>E</i> be <span>(Ftimes F)</span> (resp. a quadratic extension of <i>F</i>). We prove that an irreducible generic (resp. nearly tempered) representation of <span>(textrm{GL}_n(E))</span> is <span>(textrm{GL}_n(F))</span> distinguished if and only if its Rankin-Selberg (resp. Asai) <i>L</i>-function has an exceptional pole of level zero at 0. Further, we deduce a necessary condition for the ramification of such representations using the theory of weak test vectors developed by Humphries and Jo.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"59 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141188589","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
Étale cohomology of algebraizable rigid analytic varieties via nearby cycles over general bases 可代数刚性解析变种通过一般基上的邻近循环的Étale同调
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-05-22 DOI: 10.1007/s00229-024-01564-0
Hiroki Kato
{"title":"Étale cohomology of algebraizable rigid analytic varieties via nearby cycles over general bases","authors":"Hiroki Kato","doi":"10.1007/s00229-024-01564-0","DOIUrl":"https://doi.org/10.1007/s00229-024-01564-0","url":null,"abstract":"<p>We prove a finiteness theorem and a comparison theorem in the theory of étale cohomology of rigid analytic varieties. By a result of Huber, for a quasi-compact separated morphism of rigid analytic varieties with target being of dimension <span>(le 1)</span>, the compactly supported higher direct image preserves quasi-constructibility. Though the analogous statement for morphisms with higher dimensional target fails in general, we prove that, in the algebraizable case, it holds after replacing the target with a modification. We deduce it from a known finiteness result in the theory of nearby cycles over general bases and a new comparison result, which gives an identification of the compactly supported higher direct image sheaves, up to modification of the target, in terms of nearby cycles over general bases.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"41 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146862","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 contact varieties 奇异接触变种
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-05-20 DOI: 10.1007/s00229-024-01561-3
Robert Śmiech
{"title":"Singular contact varieties","authors":"Robert Śmiech","doi":"10.1007/s00229-024-01561-3","DOIUrl":"https://doi.org/10.1007/s00229-024-01561-3","url":null,"abstract":"<p>In this note we propose the generalization of the notion of a holomorphic contact structure on a manifold (smooth variety) to varieties with rational singularities and prove basic properties of such objects. Natural examples of <i>singular contact varieties</i> come from the theory of nilpotent orbits: every projectivization of the closure of a nilpotent orbit in a semisimple Lie algebra satisfies our definition after normalization. We show the correspondence between symplectic varieties with the structure of a <span>(mathbb {C}^*)</span>-bundle and the contact ones along with the existence of stratification <i>à la</i> Kaledin. In the projective case we demonstrate the equivalence between crepant and contact resolutions of singularities, show the uniruledness and give a full classification of projective contact varieties in dimension 3.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"143 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146982","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
Instanton sheaves on Fano threefolds 法诺三折上的瞬子切
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-05-14 DOI: 10.1007/s00229-024-01559-x
Gaia Comaschi, Marcos Jardim
{"title":"Instanton sheaves on Fano threefolds","authors":"Gaia Comaschi, Marcos Jardim","doi":"10.1007/s00229-024-01559-x","DOIUrl":"https://doi.org/10.1007/s00229-024-01559-x","url":null,"abstract":"<p>Generalizing the definitions originally presented by Kuznetsov and Faenzi, we study (possibly non locally free) instanton sheaves of arbitrary rank on Fano threefolds. We classify rank 1 instanton sheaves and describe all curves whose structure sheaves are rank 0 instanton sheaves. In addition, we show that every rank 2 instanton sheaf is an elementary transformation of a locally free instanton sheaf along a rank 0 instanton sheaf. To complete the paper, we describe the moduli space of rank 2 instanton sheaves of charge 2 on a quadric threefold <i>X</i> and show that the full moduli space of rank 2 semistable sheaves on <i>X</i> with Chern classes <span>((c_1,c_2,c_3)=(-,1,2,0))</span> is connected and contains, besides the instanton component, just one other irreducible component which is also fully described.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"22 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140927791","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
On Yau sequence over complete intersection surface singularities of Brieskorn type 关于布里斯科恩型完全交面奇点上的尤序列
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-05-11 DOI: 10.1007/s00229-024-01563-1
Fanning Meng
{"title":"On Yau sequence over complete intersection surface singularities of Brieskorn type","authors":"Fanning Meng","doi":"10.1007/s00229-024-01563-1","DOIUrl":"https://doi.org/10.1007/s00229-024-01563-1","url":null,"abstract":"<p>In this paper, we study the Yau sequence concerning the minimal cycle over complete intersection surface singularities of Brieskorn type, and consider the relations between the minimal cycle <i>A</i> and the fundamental cycle <i>Z</i>. Further, we also give the coincidence between the canonical cycles and the fundamental cycles from the Yau sequence concerning the minimal cycle.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"126 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140927798","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
Yet another proof of the density in energy of Lipschitz functions 立普次函数能量密度的另一个证明
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-05-04 DOI: 10.1007/s00229-024-01562-2
Danka Lučić, Enrico Pasqualetto
{"title":"Yet another proof of the density in energy of Lipschitz functions","authors":"Danka Lučić, Enrico Pasqualetto","doi":"10.1007/s00229-024-01562-2","DOIUrl":"https://doi.org/10.1007/s00229-024-01562-2","url":null,"abstract":"<p>We provide a new, short proof of the density in energy of Lipschitz functions into the metric Sobolev space defined by using plans with barycenter (and thus, a fortiori, into the Newtonian–Sobolev space). Our result covers first-order Sobolev spaces of exponent <span>(pin (1,infty ))</span>, defined over a complete separable metric space endowed with a boundedly-finite Borel measure. Our proof is based on a completely smooth analysis: first we reduce the problem to the Banach space setting, where we consider smooth functions instead of Lipschitz ones, then we rely on classical tools in convex analysis and on the superposition principle for normal 1-currents. Along the way, we obtain a new proof of the density in energy of smooth cylindrical functions in Sobolev spaces defined over a separable Banach space endowed with a finite Borel measure.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"499 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886648","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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