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Groups of isometries of the Cuntz algebras 昆兹代数的等距群
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2021-01-01 DOI: 10.4171/dm/856
R. Conti, S. Rossi
{"title":"Groups of isometries of the Cuntz algebras","authors":"R. Conti, S. Rossi","doi":"10.4171/dm/856","DOIUrl":"https://doi.org/10.4171/dm/856","url":null,"abstract":"","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"58 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83950529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Complete intersections of quadrics and complete intersections on Segre varieties with common specializations 二次曲线的完全相交和具有共同专门化的Segre变种的完全相交
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2021-01-01 DOI: 10.4171/dm/818
C. Peters, H. Sterk
{"title":"Complete intersections of quadrics and complete intersections on Segre varieties with common specializations","authors":"C. Peters, H. Sterk","doi":"10.4171/dm/818","DOIUrl":"https://doi.org/10.4171/dm/818","url":null,"abstract":". We investigate whether surfaces that are complete intersections of quadrics and complete intersection surfaces in the Segre embedded product P 1 × P k ֒ → P 2 k +1 can belong to the same Hilbert scheme. For k = 2 there is a classical example; it comes from K3 surfaces in projective 5-space that degenerate into a hypersurface on the Segre threefold. We show that for k ≥ 3 there is only one more example. It turns out that its (connected) Hilbert scheme has at least two irreducible components. We investigate the corresponding local moduli","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"36 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87711971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Erratum to: "Stability of equivariant vector bundles over toric varieties" 对“等变矢量束在环面品种上的稳定性”的勘误
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2021-01-01 DOI: 10.4171/dm/841
Jyotirindra Dasgupta, A. Dey, Bivas Khan
{"title":"Erratum to: \"Stability of equivariant vector bundles over toric varieties\"","authors":"Jyotirindra Dasgupta, A. Dey, Bivas Khan","doi":"10.4171/dm/841","DOIUrl":"https://doi.org/10.4171/dm/841","url":null,"abstract":"","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"5 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81481928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Iwasawa theory for symmetric squares of non-$p$-ordinary eigenforms 非p -普通特征型对称平方的Iwasawa理论
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2021-01-01 DOI: 10.4171/dm/808
Kâzım Büyükboduk, Antonio Lei, Guhan Venkat
{"title":"Iwasawa theory for symmetric squares of non-$p$-ordinary eigenforms","authors":"Kâzım Büyükboduk, Antonio Lei, Guhan Venkat","doi":"10.4171/dm/808","DOIUrl":"https://doi.org/10.4171/dm/808","url":null,"abstract":"","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"26 12 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83506936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
The "fundamental theorem" for the higher algebraic $K$-theory of strongly $mathbb{Z}$-graded rings 强$mathbb{Z}$分级环的高代数$K$理论的“基本定理”
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2021-01-01 DOI: 10.4171/dm/849
T. Hüttemann
{"title":"The \"fundamental theorem\" for the higher algebraic $K$-theory of strongly $mathbb{Z}$-graded rings","authors":"T. Hüttemann","doi":"10.4171/dm/849","DOIUrl":"https://doi.org/10.4171/dm/849","url":null,"abstract":"","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"52 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73773982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Solving the selection-recombination equation: ancestral lines and dual processes 求解选择-重组方程:祖先系和对偶过程
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2021-01-01 DOI: 10.4171/dm/829
F. Alberti, E. Baake
{"title":"Solving the selection-recombination equation: ancestral lines and dual processes","authors":"F. Alberti, E. Baake","doi":"10.4171/dm/829","DOIUrl":"https://doi.org/10.4171/dm/829","url":null,"abstract":"","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"10 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89271622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 4
On lower bounds of the dimensions of multizeta values in positive characteristic 正特征的多ζ值的维数下界
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-12-01 DOI: 10.25537/dm.2021v26.537-559
Yen-Tsung Chen, Ryotaro Harada
{"title":"On lower bounds of the dimensions of multizeta values in positive characteristic","authors":"Yen-Tsung Chen, Ryotaro Harada","doi":"10.25537/dm.2021v26.537-559","DOIUrl":"https://doi.org/10.25537/dm.2021v26.537-559","url":null,"abstract":"In this paper, we study the linear independence of special values, including the positive characteristic analogue of multizeta values, alternating multizeta values and multiple polylogarithms, at algebraic points. Consequently, we establish linearly independent sets of these values with the same weight indices and a lower bound on the dimension of the space generated by depth r > 2 multizeta values of the same weight in positive characteristic.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"16 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73139291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 5
Rational curves and strictly nef divisors on Calabi-Yau threefolds Calabi-Yau三倍上的有理曲线和严格网络因子
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-10-23 DOI: 10.25537/dm.2022v27.1581-1604
Haidong Liu, R. Svaldi
{"title":"Rational curves and strictly nef divisors on Calabi-Yau threefolds","authors":"Haidong Liu, R. Svaldi","doi":"10.25537/dm.2022v27.1581-1604","DOIUrl":"https://doi.org/10.25537/dm.2022v27.1581-1604","url":null,"abstract":"We give a criterion for a nef divisor $D$ to be semiample on a Calabi--Yau threefold $X$ when $D^3=0=c_2(X)cdot D$ and $c_3(X)neq 0$. As a direct consequence, we show that on such a variety $X$, if $D$ is strictly nef and $nu(D)neq 1$, then $D$ is ample; we also show that if there exists a nef non-ample divisor $D$ with $Dnotequiv 0$, then $X$ contains a rational curve when its topological Euler characteristic is not $0$.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"16 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77075204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 7
The theory of half derivators 半导数理论
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-10-22 DOI: 10.4171/dm/881
Ian Coley
{"title":"The theory of half derivators","authors":"Ian Coley","doi":"10.4171/dm/881","DOIUrl":"https://doi.org/10.4171/dm/881","url":null,"abstract":"We review the theory of derivators from the ground up, defining new classes of derivators which were originally motivated by derivator K-theory. We prove that many old arguments that relied on homotopical bicompleteness hold also for one-sided half derivators on arbitrary diagram categories. We end by defining the maximal domain for a K-theory of derivators generalising Waldhausen K-theory.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"6204 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79600589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl-Titchmarsh theory 矩阵弦方程对应的正则系统:一般型和显式基本解及Weyl-Titchmarsh理论
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-10-11 DOI: 10.4171/dm/823
A. Sakhnovich
{"title":"On the class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl-Titchmarsh theory","authors":"A. Sakhnovich","doi":"10.4171/dm/823","DOIUrl":"https://doi.org/10.4171/dm/823","url":null,"abstract":"An important representation of the general-type fundamental solutions of the canonical systems corresponding to matrix string equations is established using linear similarity of a certain class of Volterra operators to the squared integration. Explicit fundamental solutions of these canonical systems are also constructed via the GBDT version of Darboux transformation. Examples and applications to dynamical canonical systems are given. Explicit solutions of the dynamical canonical systems are constructed as well. Three appendices are dedicated to the Weyl--Titchmarsh theory for canonical systems, transformation of a subclass of canonical systems into matrix string equations (and of a smaller subclass of canonical systems into matrix Schrodinger equations), and a linear similarity problem for Volterra operators.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"52 1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87012366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 5
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