Pub Date : 2023-07-01DOI: 10.21099/tkbjm/20234701001
Hiroshi Sawai
The purpose in this paper is to give necessary and sufficient conditions for an LCK structure to be a Vaisman structure on a solvmanifold with a left-invariant complex structure. As an application, we determine a Vaisman solvmanifold such that the commutator of the solvable Lie group is abelian.
{"title":"VAISMAN STRUCTURES ON LCK SOLVMANIFOLDS","authors":"Hiroshi Sawai","doi":"10.21099/tkbjm/20234701001","DOIUrl":"https://doi.org/10.21099/tkbjm/20234701001","url":null,"abstract":"The purpose in this paper is to give necessary and sufficient conditions for an LCK structure to be a Vaisman structure on a solvmanifold with a left-invariant complex structure. As an application, we determine a Vaisman solvmanifold such that the commutator of the solvable Lie group is abelian.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135856108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.21099/tkbjm/20234701065
Jiryo Komeda, Makiko Mase
This article is a continuation of [4] in a way. We construct pointed curves on the K3 surfaces treated in [1] which are double covers of rational elliptic surfaces. In some cases we calculate the Weierstrass semigroups of the pointed curves. These pointed curves are the first examples on K3 surfaces that are double covers of rational elliptic surfaces such that we can calculate the Weierstrass semigroups. Moreover, we give bi-elliptic curves of genus 9 or 10 on some such K3 surfaces.
{"title":"POINTED CURVES ON K3 SURFACES WHICH ARE DOUBLE COVERS OF RATIONAL ELLIPTIC SURFACES","authors":"Jiryo Komeda, Makiko Mase","doi":"10.21099/tkbjm/20234701065","DOIUrl":"https://doi.org/10.21099/tkbjm/20234701065","url":null,"abstract":"This article is a continuation of [4] in a way. We construct pointed curves on the K3 surfaces treated in [1] which are double covers of rational elliptic surfaces. In some cases we calculate the Weierstrass semigroups of the pointed curves. These pointed curves are the first examples on K3 surfaces that are double covers of rational elliptic surfaces such that we can calculate the Weierstrass semigroups. Moreover, we give bi-elliptic curves of genus 9 or 10 on some such K3 surfaces.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135856113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.21099/tkbjm/20234701113
Yasutsugu Fujita, Maohua Le, Nobuhiro Terai
Let f, g be fixed coprime positive integers with min{f,g}>1. Recently, T. Miyazaki and N. Terai [11] conjectured that the equation fx+(f+g)y=gz has no positive integer solutions (x,y,z), except for certain known pairs (f,g). This is a problem that is far from being solved. Let r be an odd positive integer with r>1. In this paper, using Baker’s method with some known results on the generalized Lebesgue-Nagell equations, we prove that if f=2r and one of the following conditions is satisfied, then the above conjecture is true. (i) Either g or f+g has a divisor d with d≡5 or 7 (mod 8). (ii) f>22493glogg or 167748logg according to g≡1 or 3 (mod 8).
{"title":"A NOTE ON THE TERNARY PURELY EXPONENTIAL DIOPHANTINE EQUATION fx+(f+g)y=gz","authors":"Yasutsugu Fujita, Maohua Le, Nobuhiro Terai","doi":"10.21099/tkbjm/20234701113","DOIUrl":"https://doi.org/10.21099/tkbjm/20234701113","url":null,"abstract":"Let f, g be fixed coprime positive integers with min{f,g}>1. Recently, T. Miyazaki and N. Terai [11] conjectured that the equation fx+(f+g)y=gz has no positive integer solutions (x,y,z), except for certain known pairs (f,g). This is a problem that is far from being solved. Let r be an odd positive integer with r>1. In this paper, using Baker’s method with some known results on the generalized Lebesgue-Nagell equations, we prove that if f=2r and one of the following conditions is satisfied, then the above conjecture is true. (i) Either g or f+g has a divisor d with d≡5 or 7 (mod 8). (ii) f>22493glogg or 167748logg according to g≡1 or 3 (mod 8).","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135856109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.21099/tkbjm/20234701029
Kenta Tsukuura
{"title":"ON THE CENTEREDNESS OF SATURATED IDEALS","authors":"Kenta Tsukuura","doi":"10.21099/tkbjm/20234701029","DOIUrl":"https://doi.org/10.21099/tkbjm/20234701029","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135856114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.21099/tkbjm/20234701019
Yasuhito Nakajima
The Bergman fan of a matroid is the intersection of tropical hyperplanes defined by the circuits. A tropical basis is a subset of the circuit set that defines the Bergman fan. Yu and Yuster posed a question whether every simple regular matroid has a unique minimal tropical basis of its Bergman fan, and verified it for graphic, cographic matroids and R10. We show every simple binary matroid has a unique minimal tropical basis. Since the regular matroid is binary, we positively answered the question.
{"title":"MINIMAL TROPICAL BASES FOR BERGMAN FANS OF MATROIDS","authors":"Yasuhito Nakajima","doi":"10.21099/tkbjm/20234701019","DOIUrl":"https://doi.org/10.21099/tkbjm/20234701019","url":null,"abstract":"The Bergman fan of a matroid is the intersection of tropical hyperplanes defined by the circuits. A tropical basis is a subset of the circuit set that defines the Bergman fan. Yu and Yuster posed a question whether every simple regular matroid has a unique minimal tropical basis of its Bergman fan, and verified it for graphic, cographic matroids and R10. We show every simple binary matroid has a unique minimal tropical basis. Since the regular matroid is binary, we positively answered the question.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135856110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.21099/tkbjm/20234701083
Tomoya Machide
The formal multiple zeta space we consider with a computer is an F2-vector space generated by 2k−2 formal symbols for a given weight k, where the symbols satisfy binary extended double shuffle relations. Up to weight k=22, we compute the dimensions of the formal multiple zeta spaces, and verify the dimension conjecture on original extended double shuffle relations of real multiple zeta values. Our computations adopt Gaussian forward elimination and give information for spaces filtered by depth. We can observe that the dimensions of the depth-graded formal multiple zeta spaces have a Pascal triangle pattern expected by the Hoffman mult-indices.
{"title":"COMPUTATIONS ABOUT FORMAL MULTIPLE ZETA SPACES DEFINED BY BINARY EXTENDED DOUBLE SHUFFLE RELATIONS","authors":"Tomoya Machide","doi":"10.21099/tkbjm/20234701083","DOIUrl":"https://doi.org/10.21099/tkbjm/20234701083","url":null,"abstract":"The formal multiple zeta space we consider with a computer is an F2-vector space generated by 2k−2 formal symbols for a given weight k, where the symbols satisfy binary extended double shuffle relations. Up to weight k=22, we compute the dimensions of the formal multiple zeta spaces, and verify the dimension conjecture on original extended double shuffle relations of real multiple zeta values. Our computations adopt Gaussian forward elimination and give information for spaces filtered by depth. We can observe that the dimensions of the depth-graded formal multiple zeta spaces have a Pascal triangle pattern expected by the Hoffman mult-indices.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135856111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.21099/tkbjm/20234701041
Takanobu Aoyama
We consider the lattice of all compatible topologies on an arbitrary finite-dimensional vector space over a non-discrete valued field whose completion is locally compact. We construct a canonical lattice isomorphism between this lattice and the lattice of all vector subspaces of the vector space whose coefficient field is extended to the complete valued field. Moreover, using this isomorphism, we characterize the continuity of linear maps between such vector spaces, and also characterize compatible topologies that are Hausdorff.
{"title":"THE CANONICAL LATTICE ISOMORPHISM BETWEEN TOPOLOGIES COMPATIBLE WITH A VECTOR SPACE AND SUBSPACES","authors":"Takanobu Aoyama","doi":"10.21099/tkbjm/20234701041","DOIUrl":"https://doi.org/10.21099/tkbjm/20234701041","url":null,"abstract":"We consider the lattice of all compatible topologies on an arbitrary finite-dimensional vector space over a non-discrete valued field whose completion is locally compact. We construct a canonical lattice isomorphism between this lattice and the lattice of all vector subspaces of the vector space whose coefficient field is extended to the complete valued field. Moreover, using this isomorphism, we characterize the continuity of linear maps between such vector spaces, and also characterize compatible topologies that are Hausdorff.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135856112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.21099/tkbjm/20234701125
Toshikazu Miyashita
{"title":"CORRIGENDUM TO REALIZATIONS OF INNER AUTOMORPHISMS OF ORDER FOUR AND FIXED POINTS SUBGROUPS BY THEM ON THE CONNECTED COMPACT EXCEPTIONAL LIE GROUP E8 PART III, TSUKUBA J. MATH., VOL. 46, NO. 1 (2022), 39–65","authors":"Toshikazu Miyashita","doi":"10.21099/tkbjm/20234701125","DOIUrl":"https://doi.org/10.21099/tkbjm/20234701125","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135856107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-01DOI: 10.21099/tkbjm/20224602271
Yohei Ito
{"title":"Corrigendum to “$mathbb{C}$-Constructible enhanced ind-sheaves”","authors":"Yohei Ito","doi":"10.21099/tkbjm/20224602271","DOIUrl":"https://doi.org/10.21099/tkbjm/20224602271","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47274963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-01DOI: 10.21099/tkbjm/20224602217
Nobutaka Boumuki
{"title":"On the dimensions of vector spaces concerning holomorphic vector bundles over elliptic orbits","authors":"Nobutaka Boumuki","doi":"10.21099/tkbjm/20224602217","DOIUrl":"https://doi.org/10.21099/tkbjm/20224602217","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45842379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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