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Lifts of line bundles on curves on K3 surfaces K3 表面曲线上线束的提升
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2024-04-16 DOI: 10.1007/s12188-024-00275-3
Kenta Watanabe, Jiryo Komeda
{"title":"Lifts of line bundles on curves on K3 surfaces","authors":"Kenta Watanabe,&nbsp;Jiryo Komeda","doi":"10.1007/s12188-024-00275-3","DOIUrl":"10.1007/s12188-024-00275-3","url":null,"abstract":"<div><p>Let <i>X</i> be a K3 surface, let <i>C</i> be a smooth curve of genus <i>g</i> on <i>X</i>, and let <i>A</i> be a line bundle of degree <i>d</i> on <i>C</i>. Then a line bundle <i>M</i> on <i>X</i> with <span>(Motimes {mathcal {O}}_C=A)</span> is called a lift of <i>A</i>. In this paper, we prove that if the dimension of the linear system |<i>A</i>| is <span>(rge 2)</span>, <span>(g&gt;2d-3+(r-1)^2)</span>, <span>(dge 2r+4)</span>, and <i>A</i> computes the Clifford index of <i>C</i>, then there exists a base point free lift <i>M</i> of <i>A</i> such that the general member of |<i>M</i>| is a smooth curve of genus <i>r</i>. In particular, if |<i>A</i>| is a base point free net which defines a double covering <span>(pi :Clongrightarrow C_0)</span> of a smooth curve <span>(C_0subset {mathbb {P}}^2)</span> of degree <span>(kge 4)</span> branched at distinct 6<i>k</i> points on <span>(C_0)</span>, then, by using the aforementioned result, we can also show that there exists a 2:1 morphism <span>({tilde{pi }}:Xlongrightarrow {mathbb {P}}^2)</span> such that <span>({tilde{pi }}|_C=pi )</span>.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"94 1","pages":"95 - 106"},"PeriodicalIF":0.4,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140612935","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
The distribution of the multiplicative index of algebraic numbers over residue classes 代数数的乘法指数在残差类上的分布
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2024-04-09 DOI: 10.1007/s12188-024-00276-2
Pieter Moree, Antonella Perucca, Pietro Sgobba
{"title":"The distribution of the multiplicative index of algebraic numbers over residue classes","authors":"Pieter Moree,&nbsp;Antonella Perucca,&nbsp;Pietro Sgobba","doi":"10.1007/s12188-024-00276-2","DOIUrl":"10.1007/s12188-024-00276-2","url":null,"abstract":"<div><p>Let <i>K</i> be a number field and <i>G</i> a finitely generated torsion-free subgroup of <span>(K^times )</span>. Given a prime <span>(mathfrak {p})</span> of <i>K</i> we denote by <span>({{,textrm{ind},}}_mathfrak {p}(G))</span> the index of the subgroup <span>((Gbmod mathfrak {p}))</span> of the multiplicative group of the residue field at <span>(mathfrak {p})</span>. Under the Generalized Riemann Hypothesis we determine the natural density of primes of <i>K</i> for which this index is in a prescribed set <i>S</i> and has prescribed Frobenius in a finite Galois extension <i>F</i> of <i>K</i>. We study in detail the natural density in case <i>S</i> is an arithmetic progression, in particular its positivity.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"94 1","pages":"1 - 17"},"PeriodicalIF":0.4,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140595195","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
(C^{1,alpha })-regularity for p-harmonic functions on SU(3) and semi-simple Lie groups SU(3) 和半简单李群上 p 谐函数的 $$C^{1,alpha }$$ 规律性
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2024-03-18 DOI: 10.1007/s12188-024-00274-4
Chengwei Yu
{"title":"(C^{1,alpha })-regularity for p-harmonic functions on SU(3) and semi-simple Lie groups","authors":"Chengwei Yu","doi":"10.1007/s12188-024-00274-4","DOIUrl":"10.1007/s12188-024-00274-4","url":null,"abstract":"<div><p>In this paper, when <span>(1&lt;p&lt;2)</span>, we establish the <span>(C^{1,alpha }_{,textrm{loc},})</span>-regularity of weak solutions to the degenerate subelliptic <i>p</i>-Laplacian equation </p><div><div><span>$$begin{aligned} triangle _{{{mathcal {H}}},p}u(x)=sum limits _{i=1}^6X^*_i(|{nabla _{{{mathcal {H}}}}u}|^{p-2}X_iu)=0 end{aligned}$$</span></div></div><p>on SU(3) endowed with the horizontal vector fields <span>(X_1,dots ,X_6)</span>. The result can be extended to a class of compact connected semi-simple Lie group.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"94 1","pages":"57 - 94"},"PeriodicalIF":0.4,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150430","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
Biconservative surfaces with constant mean curvature in Lorentzian space forms 洛伦兹空间形式中具有恒定平均曲率的双保守曲面
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2024-01-29 DOI: 10.1007/s12188-023-00273-x
Aykut Kayhan, Nurettin Cenk Turgay
{"title":"Biconservative surfaces with constant mean curvature in Lorentzian space forms","authors":"Aykut Kayhan,&nbsp;Nurettin Cenk Turgay","doi":"10.1007/s12188-023-00273-x","DOIUrl":"10.1007/s12188-023-00273-x","url":null,"abstract":"<div><p>In this paper, we consider biconservative and biharmonic isometric immersions into the 4-dimensional Lorentzian space form <span>({mathbb {L}}^4(delta ))</span> with constant sectional curvature <span>(delta )</span>. We obtain some local classifications of biconservative CMC surfaces in <span>({mathbb {L}}^4(delta ))</span>. Further, we get complete classification of biharmonic CMC surfaces in the de Sitter 4-space. We also proved that there is no biharmonic CMC surface in the anti-de Sitter 4-space. Further, we get the classification of biconservative, quasi-minimal surfaces in Minkowski-4 space.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"94 1","pages":"19 - 31"},"PeriodicalIF":0.4,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139583144","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
Towards generic base-point-freeness for hyperkähler manifolds of generalized Kummer type 广义Kummer型hyperkähler流形的一般基点自由性
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2023-11-16 DOI: 10.1007/s12188-023-00271-z
Mauro Varesco
{"title":"Towards generic base-point-freeness for hyperkähler manifolds of generalized Kummer type","authors":"Mauro Varesco","doi":"10.1007/s12188-023-00271-z","DOIUrl":"10.1007/s12188-023-00271-z","url":null,"abstract":"<div><p>We study base-point-freeness for big and nef line bundles on hyperkähler manifolds of generalized Kummer type: For <span>(nin {2,3,4})</span>, we show that, generically in all but a finite number of irreducible components of the moduli space of polarized <span>(textrm{Kum}^n)</span>-type varieties, the polarization is base-point-free. We also prove generic base-point-freeness in the moduli space in all dimensions if the polarization has divisibility one.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"93 2","pages":"133 - 147"},"PeriodicalIF":0.4,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473078","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
Correction to: Isotropicity of surfaces in Lorentzian 4-manifolds with zero mean curvature vector 校正:具有零平均曲率矢量的洛伦兹4流形中曲面的各向同性
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2023-11-13 DOI: 10.1007/s12188-023-00272-y
Naoya Ando
{"title":"Correction to: Isotropicity of surfaces in Lorentzian 4-manifolds with zero mean curvature vector","authors":"Naoya Ando","doi":"10.1007/s12188-023-00272-y","DOIUrl":"10.1007/s12188-023-00272-y","url":null,"abstract":"","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"93 2","pages":"163 - 166"},"PeriodicalIF":0.4,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136283096","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
An example of Tateno disproving conjectures of Bonato–Tardif, Thomasse, and Tyomkyn Tateno反驳Bonato-Tardif、Thomasse和Tyomkyn猜想的一个例子
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2023-11-01 DOI: 10.1007/s12188-023-00270-0
Davoud Abdi Kalow, Claude Laflamme, Atsushi Tateno, Robert Woodrow
{"title":"An example of Tateno disproving conjectures of Bonato–Tardif, Thomasse, and Tyomkyn","authors":"Davoud Abdi Kalow,&nbsp;Claude Laflamme,&nbsp;Atsushi Tateno,&nbsp;Robert Woodrow","doi":"10.1007/s12188-023-00270-0","DOIUrl":"10.1007/s12188-023-00270-0","url":null,"abstract":"<div><p>In his 2008 thesis [16] , Tateno claimed a counterexample to the Bonato–Tardif conjecture regarding the number of equimorphy classes of trees. In this paper we revisit Tateno’s unpublished ideas to provide a rigorous exposition, constructing locally finite trees having an arbitrary finite number of equimorphy classes; an adaptation provides partial orders with a similar conclusion. At the same time these examples also disprove conjectures by Thomassé and Tyomkyn.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"93 2","pages":"99 - 131"},"PeriodicalIF":0.4,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135272208","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: 6
Lines on p-adic and real cubic surfaces p进曲面和实立方曲面上的直线
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2023-09-16 DOI: 10.1007/s12188-023-00269-7
Rida Ait El Manssour, Yassine El Maazouz, Enis Kaya, Kemal Rose
{"title":"Lines on p-adic and real cubic surfaces","authors":"Rida Ait El Manssour,&nbsp;Yassine El Maazouz,&nbsp;Enis Kaya,&nbsp;Kemal Rose","doi":"10.1007/s12188-023-00269-7","DOIUrl":"10.1007/s12188-023-00269-7","url":null,"abstract":"<div><p>We study lines on smooth cubic surfaces over the field of <i>p</i>-adic numbers, from a theoretical and computational point of view. Segre showed that the possible counts of such lines are 0, 1, 2, 3, 5, 7, 9, 15 or 27. We show that each of these counts is achieved. Probabilistic aspects are investigated by sampling both <i>p</i>-adic and real cubic surfaces from different distributions and estimating the probability of each count.We link this to recent results on probabilistic enumerative geometry. Some experimental results on the Galois groups attached to <i>p</i>-adic cubic surfaces are also discussed.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"93 2","pages":"149 - 162"},"PeriodicalIF":0.4,"publicationDate":"2023-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135305607","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 curves on Hirzebruch surfaces 在Hirzebruch曲面的曲线上
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2023-06-08 DOI: 10.1007/s12188-023-00267-9
Gerriet Martens
{"title":"On curves on Hirzebruch surfaces","authors":"Gerriet Martens","doi":"10.1007/s12188-023-00267-9","DOIUrl":"10.1007/s12188-023-00267-9","url":null,"abstract":"<div><p>We call a smooth irreducible projective curve a Castelnuovo curve if it admits a birational map into the projective r-space such that the image curve has degree at least 2r+1 and the maximum possible geometric genus (which one can calculate by a classical formula due to Castelnuovo). It is well known that a Castelnuovo curve must lie on a Hirzebruch surface (rational ruled surface). Conversely, making use of a result of W. Castryck and F. Cools concerning the scrollar invariants of curves on Hirzebruch surfaces we show that curves on Hirzebruch surfaces are Castelnuovo curves unless their genus becomes too small w.r.t. their gonality. We analyze the situation more closely, and we calculate the number of moduli of curves of fixed genus g and fixed gonality k lying on Hirzebruch surfaces, in terms of g and k.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"93 1","pages":"85 - 98"},"PeriodicalIF":0.4,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-023-00267-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50014907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Unexpected Cyclic Symmetry of (I{mathfrak u}_n) 的意外循环对称 (I{mathfrak u}_n)
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2023-03-16 DOI: 10.1007/s12188-023-00266-w
Dror Bar-Natan, Roland van der Veen
{"title":"An Unexpected Cyclic Symmetry of (I{mathfrak u}_n)","authors":"Dror Bar-Natan,&nbsp;Roland van der Veen","doi":"10.1007/s12188-023-00266-w","DOIUrl":"10.1007/s12188-023-00266-w","url":null,"abstract":"<div><p>We find and discuss an unexpected (to us) order <i>n</i> cyclic group of automorphisms of the Lie algebra <span>(I{mathfrak u}_n{:}{=}{mathfrak u}_n &lt; imes {mathfrak u}_n^*)</span>, where <span>({mathfrak u}_n)</span> is the Lie algebra of upper triangular <span>(ntimes n)</span> matrices. Our results also extend to <span>(mathfrak {gl}_{n+}^epsilon )</span>, a “solvable approximation” of <span>(mathfrak {gl}_n)</span>, as defined within.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"93 1","pages":"71 - 76"},"PeriodicalIF":0.4,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-023-00266-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50032540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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