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Geometriae Dedicata最新文献

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Construction and characterisation of the varieties of the third row of the Freudenthal–Tits magic square Freudenthal-Tits魔法广场第三排的构造和特征
IF 0.5 4区 数学 Q3 MATHEMATICS
Geometriae Dedicata
Pub Date : 2023-11-28 DOI: 10.1007/s10711-023-00864-1
Anneleen De Schepper, Jeroen Schillewaert, Hendrik Van Maldeghem, Magali Victoor

We characterise the varieties appearing in the third row of the Freudenthal–Tits magic square over an arbitrary field, in both the split and non-split version, as originally presented by Jacques Tits in his Habilitation thesis. In particular, we characterise the variety related to the 56-dimensional module of a Chevalley group of exceptional type (mathsf {E_7}) over an arbitrary field. We use an elementary axiom system which is the natural continuation of the one characterising the varieties of the second row of the magic square. We provide an explicit common construction of all characterised varieties as the quadratic Zariski closure of the image of a newly defined affine dual polar Veronese map. We also provide a construction of each of these varieties as the common null set of quadratic forms.

我们描述了在任意场上出现在Freudenthal-Tits魔方的第三排的品种，在分裂和非分裂版本中，正如雅克·Tits在他的康复论文中最初提出的那样。特别是，我们描述了在任意字段上异常类型(mathsf {E_7})的Chevalley群的56维模块相关的变化。我们使用了一个初等公理系统，它是表征幻方第二行变异的公理系统的自然延拓。我们提供了一个明确的共同结构的所有特征变种的二次Zariski闭包的图像的一个新定义仿射对偶极Veronese地图。我们还提供了这些变量作为二次型的公共零集的构造。
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引用次数: 0
Clifford structures, bilegendrian surfaces, and extrinsic curvature Clifford结构，双列曲面和外在曲率
IF 0.5 4区 数学 Q3 MATHEMATICS
Geometriae Dedicata
Pub Date : 2023-11-27 DOI: 10.1007/s10711-023-00855-2
Graham Smith

We use Clifford algebras to construct a unified formalism for studying constant extrinsic curvature immersed surfaces in Riemannian and semi-Riemannian 3-manifolds in terms of immersed bilegendrian surfaces in their unitary bundles. As an application, we provide full classifications of both complete and compact immersed bilegendrian surfaces in the unit tangent bundle ({text {U}}mathbb {S}^3) of the 3-sphere.

利用Clifford代数构造了一个统一的形式，用于研究黎曼和半黎曼3-流形中恒定外曲率浸没曲面在黎曼和半黎曼3-流形中的浸没曲面在黎曼和半黎曼3-流形中的正束浸没曲面。作为一种应用，我们在3球的单位切线束({text {U}}mathbb {S}^3)上给出了完全和紧致浸没双线曲面的完全分类。
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引用次数: 0
A Fano compactification of the $$textrm{SL}_2(mathbb {C})$$ free group character variety $$textrm{SL}_2(mathbb {C})$$自由群字符变化的Fano紧化
IF 0.5 4区 数学 Q3 MATHEMATICS
Geometriae Dedicata
Pub Date : 2023-11-23 DOI: 10.1007/s10711-023-00867-y
Joseph Cummings, Christopher Manon

We show that a certain compactification (mathfrak {X}_g) of the (textrm{SL}_2(mathbb {C})) free group character variety (mathcal {X}(F_g, textrm{SL}_2(mathbb {C}))) is Fano. This compactification has been studied previously by the second author, and separately by Biswas, Lawton, and Ramras. Part of the proof of this result involves the construction of a large family of integral reflexive polytopes.

我们证明了(textrm{SL}_2(mathbb {C}))自由群特征变化(mathcal {X}(F_g, textrm{SL}_2(mathbb {C})))的一定紧化(mathfrak {X}_g)是Fano。这种紧化已经由第二作者和Biswas、Lawton和Ramras分别研究过。这个结果的部分证明涉及到一个大族的整自反多面体的构造。
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引用次数: 0
Rigidity of geometric structures 几何结构刚度
IF 0.5 4区 数学 Q3 MATHEMATICS
Geometriae Dedicata
Pub Date : 2023-11-20 DOI: 10.1007/s10711-023-00861-4
Ursula Hamenstädt, Frieder Jäckel

Geometric structures on a manifold M arise from a covering of M by charts with values in a homogeneous space G/H, with chart transitions restrictions of elements of G. If M is aspherical, then such geometric structures are given by a homomorphism of the fundamental group of M into G. Rigidity of such structures means that the conjugacy class of the homomorphism can be reconstructed from topological or geometric information on M. We give an overview of such rigidity results, focusing on topological type and length functions.

流形M上的几何结构是由具有齐次空间G/H中值的图对M的覆盖而产生的，具有G元素的图迁移限制。如果M是非球面的，则这种几何结构由M的基本群与G的同态给出。这种结构的刚性意味着同态的共轭类可以由M上的拓扑或几何信息重构。着重于拓扑类型和长度函数。
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引用次数: 0
Tent property of the growth indicator functions and applications 帐篷性质的生长指标的功能及应用
4区 数学 Q3 MATHEMATICS
Geometriae Dedicata
Pub Date : 2023-11-14 DOI: 10.1007/s10711-023-00846-3
Dongryul M. Kim, Yair N. Minsky, Hee Oh
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引用次数: 15
On the cohomology of character stacks for non-orientable surfaces 非定向曲面上字符堆的上同调性
4区 数学 Q3 MATHEMATICS
Geometriae Dedicata
Pub Date : 2023-11-10 DOI: 10.1007/s10711-023-00863-2
Tommaso Scognamiglio
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引用次数: 0
A structure theorem and left-orderability of a quotient of quasi-isometry group of the real line 实线拟等距群商的结构定理及左序性
4区 数学 Q3 MATHEMATICS
Geometriae Dedicata
Pub Date : 2023-11-07 DOI: 10.1007/s10711-023-00857-0
Swarup Bhowmik, Prateep Chakraborty
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引用次数: 0
Orthogonal ring patterns in the plane 平面上的正交环形图案
4区 数学 Q3 MATHEMATICS
Geometriae Dedicata
Pub Date : 2023-11-03 DOI: 10.1007/s10711-023-00859-y
Alexander I. Bobenko, Tim Hoffmann, Thilo Rörig
Abstract We introduce orthogonal ring patterns consisting of pairs of concentric circles generalizing circle patterns. We show that orthogonal ring patterns are governed by the same equation as circle patterns. For every ring pattern there exists a one parameter family of patterns that interpolates between a circle pattern and its dual. We construct ring patterns analogues of the Doyle spiral, Erf and $$z^alpha $$ z α functions. We also derive a variational principle and compute ring patterns based on Dirichlet and Neumann boundary conditions.
摘要推广圆图案，引入由同心圆对组成的正交环图案。我们证明正交环形图案与圆形图案由相同的方程控制。对于每一个环状图案，都存在一个参数族的图案，它插在圆形图案和它的对偶图案之间。我们构造了类似Doyle螺旋、Erf和$$z^alpha $$ z α函数的环状图案。我们还推导了基于Dirichlet和Neumann边界条件的变分原理并计算了环图案。
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引用次数: 0
A natural compactification of the Gromov–Hausdorff space Gromov-Hausdorff空间的一个自然紧化
4区 数学 Q3 MATHEMATICS
Geometriae Dedicata
Pub Date : 2023-11-02 DOI: 10.1007/s10711-023-00852-5
Hiroki Nakajima, Takashi Shioya
{"title":"A natural compactification of the Gromov–Hausdorff space","authors":"Hiroki Nakajima, Takashi Shioya","doi":"10.1007/s10711-023-00852-5","DOIUrl":"https://doi.org/10.1007/s10711-023-00852-5","url":null,"abstract":"","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"17 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135874755","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
Stars at infinity for boundaries of Teichmüller space 无限远处的恒星在泰希<s:1>勒空间的边界
4区 数学 Q3 MATHEMATICS
Geometriae Dedicata
Pub Date : 2023-10-31 DOI: 10.1007/s10711-023-00853-4
Peijia Liu, Yaozhong Shi
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引用次数: 0
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