{"title":"Note on class number parity of an abelian field of prime conductor, II","authors":"H. Ichimura","doi":"10.2996/kmj/1552982508","DOIUrl":"https://doi.org/10.2996/kmj/1552982508","url":null,"abstract":"","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43287061","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}
We study families of $K3$ surfaces obtained by double covering of the projective plane branching along curves of $(2,3)$-torus type. In the first part, we study the Picard lattices of the families, and a lattice duality of them. In the second part, we describe a deformation of singularities of Gorenstein $K3$ surfaces in these families.
{"title":"Families of $K3$ surfaces and curves of (2,3)-torus type","authors":"Makiko Mase","doi":"10.2996/kmj/1572487224","DOIUrl":"https://doi.org/10.2996/kmj/1572487224","url":null,"abstract":"We study families of $K3$ surfaces obtained by double covering of the projective plane branching along curves of $(2,3)$-torus type. In the first part, we study the Picard lattices of the families, and a lattice duality of them. In the second part, we describe a deformation of singularities of Gorenstein $K3$ surfaces in these families.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48030635","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}
We prove that a projective vertical exact log smooth morphism of fs log analytic spaces with a base of log rank one yields polarized log Hodge structures in the canonical way.
{"title":"Geometric polarized log Hodge structures with a base of log rank one","authors":"T. Fujisawa, Chikara Nakayama","doi":"10.2996/kmj/1584345688","DOIUrl":"https://doi.org/10.2996/kmj/1584345688","url":null,"abstract":"We prove that a projective vertical exact log smooth morphism of fs log analytic spaces with a base of log rank one yields polarized log Hodge structures in the canonical way.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2018-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46370108","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}
Let $G$ be a compact Lie group and $T$ its maximal torus. In this paper, we try to compute $gr_{gamma}^*(G/T)$ the graded ring associated with the gamma filtration of the complex $K$-theory $K^0(G/T)$ for $G=Spin(n)$. In particular, we give a counterexample for a conjecture by Karpenko when $G=Spin(17)$. The arguments for $E_7$ in $S 11$ of the old version were not correct, and they are deleted in this version.
{"title":"The gamma filtrations for the spin groups","authors":"N. Yagita","doi":"10.2996/kmj44109","DOIUrl":"https://doi.org/10.2996/kmj44109","url":null,"abstract":"Let $G$ be a compact Lie group and $T$ its maximal torus. In this paper, we try to compute $gr_{gamma}^*(G/T)$ the graded ring associated with the gamma filtration of the complex $K$-theory $K^0(G/T)$ for $G=Spin(n)$. In particular, we give a counterexample for a conjecture by Karpenko when $G=Spin(17)$. The arguments for $E_7$ in $S 11$ of the old version were not correct, and they are deleted in this version.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2018-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47828733","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}
{"title":"A new formula for the spherical growth series of an amalgamated free product of two infinite cyclic groups","authors":"Michihiko Fujii","doi":"10.2996/KMJ/1540951250","DOIUrl":"https://doi.org/10.2996/KMJ/1540951250","url":null,"abstract":"","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2996/KMJ/1540951250","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47753725","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}
{"title":"$q$-series reciprocities and further $pi$-formulae","authors":"W. Chu","doi":"10.2996/KMJ/1540951251","DOIUrl":"https://doi.org/10.2996/KMJ/1540951251","url":null,"abstract":"","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2996/KMJ/1540951251","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41542461","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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