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Hyperbolic torsion polynomials of pretzel knots 椒盐卷饼结的双曲扭转多项式
IF 0.5 4区 数学
Advances in Geometry Pub Date : 2021-04-01 DOI: 10.1515/advgeom-2020-0017
Takayuki Morifuji, Anh T. Tran
{"title":"Hyperbolic torsion polynomials of pretzel knots","authors":"Takayuki Morifuji, Anh T. Tran","doi":"10.1515/advgeom-2020-0017","DOIUrl":"https://doi.org/10.1515/advgeom-2020-0017","url":null,"abstract":"Abstract In this paper, we explicitly calculate the highest degree term of the hyperbolic torsion polynomial of an infinite family of pretzel knots. This gives supporting evidence for a conjecture of Dunfield, Friedl and Jackson that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot. The verification of the genus part of the conjecture for this family of knots also follows from the work of Agol and Dunfield [1] or Porti [19].","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":"21 1","pages":"265 - 272"},"PeriodicalIF":0.5,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/advgeom-2020-0017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43297894","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
Double cover K3 surfaces of Hirzebruch surfaces Hirzebruch表面的双层K3表面
IF 0.5 4区 数学
Advances in Geometry Pub Date : 2021-04-01 DOI: 10.1515/advgeom-2020-0034
Taro Hayashi
{"title":"Double cover K3 surfaces of Hirzebruch surfaces","authors":"Taro Hayashi","doi":"10.1515/advgeom-2020-0034","DOIUrl":"https://doi.org/10.1515/advgeom-2020-0034","url":null,"abstract":"Abstract General K3 surfaces obtained as double covers of the n-th Hirzebruch surfaces with n = 0, 1, 4 are not double covers of other smooth surfaces. We give a criterion for such a K3 surface to be a double covering of another smooth rational surface based on the branch locus of double covers and fibre spaces of Hirzebruch surfaces.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":"21 1","pages":"221 - 225"},"PeriodicalIF":0.5,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/advgeom-2020-0034","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44133106","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: 2
Exotic Steiner chains in Miquelian Möbius planes of odd order 米克尔Möbius奇阶平面中的奇异斯坦纳链
IF 0.5 4区 数学
Advances in Geometry Pub Date : 2021-04-01 DOI: 10.1515/advgeom-2020-0035
N. Hungerbühler, Gideon Villiger
{"title":"Exotic Steiner chains in Miquelian Möbius planes of odd order","authors":"N. Hungerbühler, Gideon Villiger","doi":"10.1515/advgeom-2020-0035","DOIUrl":"https://doi.org/10.1515/advgeom-2020-0035","url":null,"abstract":"Abstract In the Euclidean plane, two circles that intersect or are tangent clearly do not carry a finite Steiner chain of circles. We show that such exotic Steiner chains exist in finite Miquelian Möbius planes of odd order. We obtain explicit conditions in terms of the order of the plane and the capacitance of the two carrier circles for the existence, length, and number of Steiner chains.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":"21 1","pages":"207 - 220"},"PeriodicalIF":0.5,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/advgeom-2020-0035","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47631427","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
Fano fourfolds having a prime divisor of Picard number 1 具有皮卡德数1的素数因子的法诺四倍
IF 0.5 4区 数学
Advances in Geometry Pub Date : 2021-03-30 DOI: 10.1515/advgeom-2023-0002
S. A. Secci
{"title":"Fano fourfolds having a prime divisor of Picard number 1","authors":"S. A. Secci","doi":"10.1515/advgeom-2023-0002","DOIUrl":"https://doi.org/10.1515/advgeom-2023-0002","url":null,"abstract":"Abstract We prove a classification result for smooth complex Fano fourfolds of Picard number 3 having a prime divisor of Picard number 1, after a characterisation result in arbitrary dimension by Casagrande and Druel [5]. These varieties are obtained by blowing-up a ℙ1-bundle over a smooth Fano variety of Picard number 1 along a codimension 2 subvariety. We study in detail the case of dimension 4, and show that they form 28 families. We compute the main numerical invariants, determine the base locus of the anticanonical system, and study their deformations to give an upper bound to the dimension of the base of the Kuranishi family of a general member.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":"23 1","pages":"267 - 280"},"PeriodicalIF":0.5,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46339592","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: 3
Hodge numbers of hypersurfaces in ℙ4 with ordinary triple points 具有普通三重点的超曲面的霍奇数
IF 0.5 4区 数学
Advances in Geometry Pub Date : 2021-03-11 DOI: 10.1515/advgeom-2020-0020
S. Cynk
{"title":"Hodge numbers of hypersurfaces in ℙ4 with ordinary triple points","authors":"S. Cynk","doi":"10.1515/advgeom-2020-0020","DOIUrl":"https://doi.org/10.1515/advgeom-2020-0020","url":null,"abstract":"Abstract We give a formula for the Hodge numbers of a three-dimensional hypersurface in a weighted projective space with only ordinary triple points as singularities.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":"21 1","pages":"293 - 298"},"PeriodicalIF":0.5,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/advgeom-2020-0020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47410888","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: 2
Triharmonic Riemannian submersions from 3-dimensional space forms 三维空间形式的三谐黎曼淹没
IF 0.5 4区 数学
Advances in Geometry Pub Date : 2021-02-05 DOI: 10.1515/advgeom-2020-0033
Tomoya Miura, S. Maeta
{"title":"Triharmonic Riemannian submersions from 3-dimensional space forms","authors":"Tomoya Miura, S. Maeta","doi":"10.1515/advgeom-2020-0033","DOIUrl":"https://doi.org/10.1515/advgeom-2020-0033","url":null,"abstract":"Abstract We show that any triharmonic Riemannian submersion from a 3-dimensional space form into a surface is harmonic. This is an affirmative partial answer to the submersion version of the generalized Chen conjecture. Moreover, a non-existence theorem for f -biharmonic Riemannian submersions is also presented.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":" 19","pages":"163 - 168"},"PeriodicalIF":0.5,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/advgeom-2020-0033","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41311219","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
Chow groups of Gushel–Mukai fivefolds 周氏组的古谢尔-穆凯五倍
IF 0.5 4区 数学
Advances in Geometry Pub Date : 2021-01-14 DOI: 10.1515/advgeom-2023-0005
Lin Zhou
{"title":"Chow groups of Gushel–Mukai fivefolds","authors":"Lin Zhou","doi":"10.1515/advgeom-2023-0005","DOIUrl":"https://doi.org/10.1515/advgeom-2023-0005","url":null,"abstract":"Abstract We compute the Chow groups of smooth Gushel–Mukai varieties of dimension 5.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":"23 1","pages":"295 - 303"},"PeriodicalIF":0.5,"publicationDate":"2021-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46560440","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
A new axiomatics for masures II 测度的新公理2
IF 0.5 4区 数学
Advances in Geometry Pub Date : 2021-01-14 DOI: 10.1515/advgeom-2022-0013
Auguste Hébert
{"title":"A new axiomatics for masures II","authors":"Auguste Hébert","doi":"10.1515/advgeom-2022-0013","DOIUrl":"https://doi.org/10.1515/advgeom-2022-0013","url":null,"abstract":"Abstract Masures are generalizations of Bruhat–Tits buildings. They were introduced by Gaussent and Rousseau in order to study Kac–Moody groups over valued fields. We prove that the intersection of two apartments of a masure is convex. Using this, we simplify the axiomatic definition of masures given by Rousseau.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":"22 1","pages":"513 - 522"},"PeriodicalIF":0.5,"publicationDate":"2021-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47461537","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
Birational models of 𝓜2,2 arising as moduli of curves with nonspecial divisors 以非特殊因子曲线模形式出现的𝓜2,2的二元模型
IF 0.5 4区 数学
Advances in Geometry Pub Date : 2021-01-01 DOI: 10.1515/advgeom-2020-0026
Drew Johnson, A. Polishchuk
{"title":"Birational models of 𝓜2,2 arising as moduli of curves with nonspecial divisors","authors":"Drew Johnson, A. Polishchuk","doi":"10.1515/advgeom-2020-0026","DOIUrl":"https://doi.org/10.1515/advgeom-2020-0026","url":null,"abstract":"Abstract We study birational projective models of 𝓜2,2 obtained from the moduli space of curves with nonspecial divisors. We describe geometrically which singular curves appear in these models and show that one of them is obtained by blowing down the Weierstrass divisor in the moduli stack of 𝓩-stable curves 𝓜2,2(𝓩) defined by Smyth. As a corollary, we prove projectivity of the coarse moduli space M2,2(𝓩).","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":"21 1","pages":"23 - 43"},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/advgeom-2020-0026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41378364","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: 2
Frontmatter Frontmatter
IF 0.5 4区 数学
Advances in Geometry Pub Date : 2021-01-01 DOI: 10.1515/advgeom-2021-frontmatter1
{"title":"Frontmatter","authors":"","doi":"10.1515/advgeom-2021-frontmatter1","DOIUrl":"https://doi.org/10.1515/advgeom-2021-frontmatter1","url":null,"abstract":"","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/advgeom-2021-frontmatter1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46825967","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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