Pub Date : 2023-10-24DOI: 10.1007/s10711-023-00848-1
Indranil Biswas, Jacques Hurtubise, Vladimir Roubtsov
{"title":"Vector bundles and connections on Riemann surfaces with projective structure","authors":"Indranil Biswas, Jacques Hurtubise, Vladimir Roubtsov","doi":"10.1007/s10711-023-00848-1","DOIUrl":"https://doi.org/10.1007/s10711-023-00848-1","url":null,"abstract":"","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"1 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135220356","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}
Pub Date : 2023-10-24DOI: 10.1007/s10711-023-00851-6
Claudio Fontanari
Abstract We prove that the space of holomorphic p -forms on the moduli space $$overline{mathcal {M}}_{g,n}$$ M¯g,n of stable curves of genus g with n marked points vanishes for $$p=14, 16, 18$$ p=14,16,18 unconditionally and also for $$p=20$$ p=20 under a natural assumption in the case $$g=3$$ g=3 . This result is consistent with the Langlands program and it is obtained by applying the Arbarello–Cornalba inductive approach to the cohomology of moduli spaces.
摘要证明了在模空间$$overline{mathcal {M}}_{g,n}$$ M¯g, n上有n个标记点的g属稳定曲线的全纯p -形式空间对于$$p=14, 16, 18$$ p = 14,16,18无条件地消失，对于$$p=20$$ p = 20在一个自然假设下$$g=3$$ g = 3也无条件地消失。这一结果与Langlands规划一致，并通过对模空间上同调的Arbarello-Cornalba归纳方法得到。
{"title":"Holomorphic differential forms on moduli spaces of stable curves","authors":"Claudio Fontanari","doi":"10.1007/s10711-023-00851-6","DOIUrl":"https://doi.org/10.1007/s10711-023-00851-6","url":null,"abstract":"Abstract We prove that the space of holomorphic p -forms on the moduli space $$overline{mathcal {M}}_{g,n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mover> <mml:mi>M</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> </mml:math> of stable curves of genus g with n marked points vanishes for $$p=14, 16, 18$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>14</mml:mn> <mml:mo>,</mml:mo> <mml:mn>16</mml:mn> <mml:mo>,</mml:mo> <mml:mn>18</mml:mn> </mml:mrow> </mml:math> unconditionally and also for $$p=20$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>20</mml:mn> </mml:mrow> </mml:math> under a natural assumption in the case $$g=3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> . This result is consistent with the Langlands program and it is obtained by applying the Arbarello–Cornalba inductive approach to the cohomology of moduli spaces.","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"64 18","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135267099","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}
Pub Date : 2023-10-24DOI: 10.1007/s10711-023-00856-1
Zhongzi Wang, Ying Zhang
{"title":"Length minima for an infinite family of filling closed curves on a one-holed torus","authors":"Zhongzi Wang, Ying Zhang","doi":"10.1007/s10711-023-00856-1","DOIUrl":"https://doi.org/10.1007/s10711-023-00856-1","url":null,"abstract":"","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"2016 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135268172","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}
Pub Date : 2023-10-24DOI: 10.1007/s10711-023-00841-8
Shaked Bader, Nir Lazarovich
Abstract Median spaces are spaces in which for every three points the three intervals between them intersect at a single point. It is well known that rank-1 affine buildings are median spaces, but by a result of Haettel, higher rank buildings are not even coarse median. We define the notion of “2-median space”, which roughly says that for every four points the minimal discs filling the four geodesic triangles they span intersect in a point or a geodesic segment. We show that CAT(0) Euclidean polygonal complexes, and in particular rank-2 affine buildings, are 2-median. In the appendix, we recover a special case of a result of Stadler of a Fary–Milnor type theorem and show in elementary tools that a minimal disc filling a geodesic triangle is injective.
{"title":"Cat(0) polygonal complexes are 2-median","authors":"Shaked Bader, Nir Lazarovich","doi":"10.1007/s10711-023-00841-8","DOIUrl":"https://doi.org/10.1007/s10711-023-00841-8","url":null,"abstract":"Abstract Median spaces are spaces in which for every three points the three intervals between them intersect at a single point. It is well known that rank-1 affine buildings are median spaces, but by a result of Haettel, higher rank buildings are not even coarse median. We define the notion of “2-median space”, which roughly says that for every four points the minimal discs filling the four geodesic triangles they span intersect in a point or a geodesic segment. We show that CAT(0) Euclidean polygonal complexes, and in particular rank-2 affine buildings, are 2-median. In the appendix, we recover a special case of a result of Stadler of a Fary–Milnor type theorem and show in elementary tools that a minimal disc filling a geodesic triangle is injective.","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"34 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135267096","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}
Pub Date : 2023-10-18DOI: 10.1007/s10711-023-00844-5
Yota Maeda
{"title":"Uniruledness of some low-dimensional ball quotients","authors":"Yota Maeda","doi":"10.1007/s10711-023-00844-5","DOIUrl":"https://doi.org/10.1007/s10711-023-00844-5","url":null,"abstract":"","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135823790","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}
Pub Date : 2023-10-16DOI: 10.1007/s10711-023-00845-4
Clément de Seguins Pazzis
{"title":"Products of two involutions in orthogonal and symplectic groups","authors":"Clément de Seguins Pazzis","doi":"10.1007/s10711-023-00845-4","DOIUrl":"https://doi.org/10.1007/s10711-023-00845-4","url":null,"abstract":"","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"262 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136113949","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}
Pub Date : 2023-10-13DOI: 10.1007/s10711-023-00849-0
Genyle Nascimento
{"title":"Monodromies of projective structures on surface of finite-type","authors":"Genyle Nascimento","doi":"10.1007/s10711-023-00849-0","DOIUrl":"https://doi.org/10.1007/s10711-023-00849-0","url":null,"abstract":"","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135805174","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}
Pub Date : 2023-10-10DOI: 10.1007/s10711-023-00830-x
Herman Gluck, Jingye Yang
{"title":"Great circle fibrations and contact structures on odd-dimensional spheres","authors":"Herman Gluck, Jingye Yang","doi":"10.1007/s10711-023-00830-x","DOIUrl":"https://doi.org/10.1007/s10711-023-00830-x","url":null,"abstract":"","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136254962","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}
Pub Date : 2023-10-07DOI: 10.1007/s10711-023-00837-4
Tatsumasa Suzuki
Abstract The boundary sum of the product of a circle with a 3-ball and the product of a disk with a 2-sphere is called a pochette. Pochette surgery, which was discovered by Iwase and Matsumoto, is a generalization of Gluck surgery and a special case of torus surgery. For a pochette P embedded in a 4-manifold X , a pochette surgery on X is the operation of removing the interior of P and gluing P by a diffeomorphism of the boundary of P . We present an explicit diffeomorphism of the boundary of P for constructing a 4-manifold after any pochette surgery. We also describe a necessary and sufficient condition for some pochette surgeries on any simply-connected closed 4-manifold create a 4-manifold with the same homotopy type of the original 4-manifold. In this paper we construct infinitely many embeddings of a pochette into the 4-sphere and prove that homotopy 4-spheres obtained from surgeries along these embedded pochettes are all diffeomorphic to the 4-sphere by some explicit handle calculus and relative handle calculus.
{"title":"Constructions of homotopy 4-spheres by pochette surgery","authors":"Tatsumasa Suzuki","doi":"10.1007/s10711-023-00837-4","DOIUrl":"https://doi.org/10.1007/s10711-023-00837-4","url":null,"abstract":"Abstract The boundary sum of the product of a circle with a 3-ball and the product of a disk with a 2-sphere is called a pochette. Pochette surgery, which was discovered by Iwase and Matsumoto, is a generalization of Gluck surgery and a special case of torus surgery. For a pochette P embedded in a 4-manifold X , a pochette surgery on X is the operation of removing the interior of P and gluing P by a diffeomorphism of the boundary of P . We present an explicit diffeomorphism of the boundary of P for constructing a 4-manifold after any pochette surgery. We also describe a necessary and sufficient condition for some pochette surgeries on any simply-connected closed 4-manifold create a 4-manifold with the same homotopy type of the original 4-manifold. In this paper we construct infinitely many embeddings of a pochette into the 4-sphere and prove that homotopy 4-spheres obtained from surgeries along these embedded pochettes are all diffeomorphic to the 4-sphere by some explicit handle calculus and relative handle calculus.","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135254980","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}
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