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Geometriae Dedicata最新文献

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Inversion maps and torus actions on rational homogeneous varieties 有理齐次变异上的反演映射和环面作用
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2023-11-29 DOI: 10.1007/s10711-023-00866-z
Alberto Franceschini, Luis E. Solá Conde
{"title":"Inversion maps and torus actions on rational homogeneous varieties","authors":"Alberto Franceschini, Luis E. Solá Conde","doi":"10.1007/s10711-023-00866-z","DOIUrl":"https://doi.org/10.1007/s10711-023-00866-z","url":null,"abstract":"<p>Complex projective algebraic varieties with <span>({{mathbb {C}}}^*)</span>-actions can be thought of as geometric counterparts of birational transformations. In this paper we describe geometrically the birational transformations associated to rational homogeneous varieties endowed with a <span>({{mathbb {C}}}^*)</span>-action with no proper isotropy subgroups.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138504894","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: 1
On a convexity property of the space of almost fuchsian immersions 关于几乎紫红色浸没空间的凸性
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2023-11-28 DOI: 10.1007/s10711-023-00865-0
Samuel Bronstein, Graham Andrew Smith
{"title":"On a convexity property of the space of almost fuchsian immersions","authors":"Samuel Bronstein, Graham Andrew Smith","doi":"10.1007/s10711-023-00865-0","DOIUrl":"https://doi.org/10.1007/s10711-023-00865-0","url":null,"abstract":"<p>We study the space of Hopf differentials of almost fuchsian minimal immersions of compact Riemann surfaces. We show that the extrinsic curvature of the immersion at any given point is a concave function of the Hopf differential. As a consequence, we show that the set of all such Hopf differentials is a convex subset of the space of holomorphic quadratic differentials of the surface. In addition, we address the non-equivariant case, and obtain lower and upper bounds for the size of this set.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138504919","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
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
Geometriae Dedicata Pub Date : 2023-11-28 DOI: 10.1007/s10711-023-00864-1
Anneleen De Schepper, Jeroen Schillewaert, Hendrik Van Maldeghem, Magali Victoor
{"title":"Construction and characterisation of the varieties of the third row of the Freudenthal–Tits magic square","authors":"Anneleen De Schepper, Jeroen Schillewaert, Hendrik Van Maldeghem, Magali Victoor","doi":"10.1007/s10711-023-00864-1","DOIUrl":"https://doi.org/10.1007/s10711-023-00864-1","url":null,"abstract":"<p>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 <span>(mathsf {E_7})</span> 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.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138504895","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
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
Geometriae Dedicata Pub Date : 2023-11-27 DOI: 10.1007/s10711-023-00855-2
Graham Smith
{"title":"Clifford structures, bilegendrian surfaces, and extrinsic curvature","authors":"Graham Smith","doi":"10.1007/s10711-023-00855-2","DOIUrl":"https://doi.org/10.1007/s10711-023-00855-2","url":null,"abstract":"<p>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 <span>({text {U}}mathbb {S}^3)</span> of the 3-sphere.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138504911","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 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
Geometriae Dedicata Pub Date : 2023-11-23 DOI: 10.1007/s10711-023-00867-y
Joseph Cummings, Christopher Manon
{"title":"A Fano compactification of the $$textrm{SL}_2(mathbb {C})$$ free group character variety","authors":"Joseph Cummings, Christopher Manon","doi":"10.1007/s10711-023-00867-y","DOIUrl":"https://doi.org/10.1007/s10711-023-00867-y","url":null,"abstract":"<p>We show that a certain compactification <span>(mathfrak {X}_g)</span> of the <span>(textrm{SL}_2(mathbb {C}))</span> free group character variety <span>(mathcal {X}(F_g, textrm{SL}_2(mathbb {C})))</span> 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.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138504896","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
Rigidity of geometric structures 几何结构刚度
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2023-11-20 DOI: 10.1007/s10711-023-00861-4
Ursula Hamenstädt, Frieder Jäckel
{"title":"Rigidity of geometric structures","authors":"Ursula Hamenstädt, Frieder Jäckel","doi":"10.1007/s10711-023-00861-4","DOIUrl":"https://doi.org/10.1007/s10711-023-00861-4","url":null,"abstract":"<p>Geometric structures on a manifold <i>M</i> arise from a covering of <i>M</i> by charts with values in a homogeneous space <i>G</i>/<i>H</i>, with chart transitions restrictions of elements of <i>G</i>. If <i>M</i> is aspherical, then such geometric structures are given by a homomorphism of the fundamental group of <i>M</i> into <i>G</i>. Rigidity of such structures means that the conjugacy class of the homomorphism can be reconstructed from topological or geometric information on <i>M</i>. We give an overview of such rigidity results, focusing on topological type and length functions.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138504881","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
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
Geometriae Dedicata Pub Date : 2023-11-14 DOI: 10.1007/s10711-023-00846-3
Dongryul M. Kim, Yair N. Minsky, Hee Oh
{"title":"Tent property of the growth indicator functions and applications","authors":"Dongryul M. Kim, Yair N. Minsky, Hee Oh","doi":"10.1007/s10711-023-00846-3","DOIUrl":"https://doi.org/10.1007/s10711-023-00846-3","url":null,"abstract":"","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134900581","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: 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
Geometriae Dedicata Pub Date : 2023-11-10 DOI: 10.1007/s10711-023-00863-2
Tommaso Scognamiglio
{"title":"On the cohomology of character stacks for non-orientable surfaces","authors":"Tommaso Scognamiglio","doi":"10.1007/s10711-023-00863-2","DOIUrl":"https://doi.org/10.1007/s10711-023-00863-2","url":null,"abstract":"","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135137550","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 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
Geometriae Dedicata Pub Date : 2023-11-07 DOI: 10.1007/s10711-023-00857-0
Swarup Bhowmik, Prateep Chakraborty
{"title":"A structure theorem and left-orderability of a quotient of quasi-isometry group of the real line","authors":"Swarup Bhowmik, Prateep Chakraborty","doi":"10.1007/s10711-023-00857-0","DOIUrl":"https://doi.org/10.1007/s10711-023-00857-0","url":null,"abstract":"","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135476181","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
Orthogonal ring patterns in the plane 平面上的正交环形图案
4区 数学
Geometriae Dedicata Pub Date : 2023-11-03 DOI: 10.1007/s10711-023-00859-y
Alexander I. Bobenko, Tim Hoffmann, Thilo Rörig
{"title":"Orthogonal ring patterns in the plane","authors":"Alexander I. Bobenko, Tim Hoffmann, Thilo Rörig","doi":"10.1007/s10711-023-00859-y","DOIUrl":"https://doi.org/10.1007/s10711-023-00859-y","url":null,"abstract":"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 $$z^alpha $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>z</mml:mi> <mml:mi>α</mml:mi> </mml:msup> </mml:math> functions. We also derive a variational principle and compute ring patterns based on Dirichlet and Neumann boundary conditions.","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135868457","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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