{"title":"On the Structure of Generalized Polarized Manifolds with Relatively Small Second Class","authors":"A. Lanteri, A. L. Tironi","doi":"10.3836/tjm/1502179348","DOIUrl":"https://doi.org/10.3836/tjm/1502179348","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70165819","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":"On the Motive of Codimension 2 Linear Sections of $mathrm{Gr}(3,6)$","authors":"R. Laterveer","doi":"10.3836/tjm/1502179351","DOIUrl":"https://doi.org/10.3836/tjm/1502179351","url":null,"abstract":"We consider Fano sevenfolds $Y$ obtained by intersecting the Grassmannian $mathrm{Gr}(3,6)$ with a codimension 2 linear subspace (with respect to the Pl\"ucker embedding). We prove that the motive of $Y$ is Kimura finite-dimensional. We also prove the generalized Hodge conjecture for all powers of $Y$.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41746515","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":"Some Results on Invariant Measures for $1$-dimensional Maps","authors":"F. Schweiger","doi":"10.3836/tjm/1502179353","DOIUrl":"https://doi.org/10.3836/tjm/1502179353","url":null,"abstract":"For many fibred systems the existence of an invariant measure can be proved but considerably less is known about the shape of the density. In this note various examples of invariant densities are discussed: Piecewise fractional linear maps with four branches and maps which are associated to continued fractions with increasing digits. There are ergodic maps with a non-integrable density which do not have an indifferent fixed point and maps such that the set of points which miss the digit $k=1$ has positive Lebesgue measure.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46292721","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":"The Diophantine Equation $X^3=u+v$ over Real Quadratic Fields, II","authors":"T. Kagawa","doi":"10.3836/tjm/1502179345","DOIUrl":"https://doi.org/10.3836/tjm/1502179345","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43019663","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":"On the $lambda$-invariant of Selmer Groups Arising from Certain Quadratic Twists of Gross Curves","authors":"Jianing Li","doi":"10.3836/tjm/1502179379","DOIUrl":"https://doi.org/10.3836/tjm/1502179379","url":null,"abstract":"Let q be a prime with q ≡ 7 mod 8, and let K = Q( √ −q). Then 2 splits in K, and we write p for either of the primes K above 2. Let K∞ be the unique Z2-extension of K unramified outside p with n-th layer Kn. For certain quadratic and biquadratic extensions F/K, we prove a simple exact formula for the λ-invariant of the Galois group of the maximal abelian 2-extension unramified outside p of the field F∞ = FK∞. Equivalently, our result determines the exact Z2-corank of certain Selmer groups over F∞ of a large family of quadratic twists of the higher dimensional abelian variety with complex multiplication, which is the restriction of scalars to K of the Gross curve with complex multiplication defined over the Hilbert class field of K. We also discuss computations of the associated Selmer groups over Kn in the case when the λ-invariant is equal to 1.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44368783","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}
Minoru Tanaka, T. Akamatsu, R. Sinclair, M. Yamaguchi
{"title":"A New Family of Latitudinally Corrugated Two-spheres of Revolution with Simple Cut Locus Structure","authors":"Minoru Tanaka, T. Akamatsu, R. Sinclair, M. Yamaguchi","doi":"10.3836/tjm/1502179366","DOIUrl":"https://doi.org/10.3836/tjm/1502179366","url":null,"abstract":"There are not so many kinds of surface of revolution whose cut locus structure have been determined, although the cut locus structures of very familiar surfaces of revolution (in Euclidean space) such as ellipsoids, 2-sheeted hyperboloids, paraboloids and tori are now known. Except for tori, the known cut locus structures are very simple, i.e., a single point or an arc. In this article, a new family {Mn}n of 2-spheres of revolution with simple cut locus structure is introduced. This family is also new in the sense that the number of points on each meridian which assume a local minimum or maximum of the Gaussian curvature function on the meridian goes to infinity as n tends to infinity. Thus, our family includes surfaces which have arbitrarily many bands of alternately increasing or decreasing Gaussian curvature, although each member of this family has a simple cut locus structure.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":"32 1-2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41307926","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":"On Syntomic Complexes with Modulus for Semi-stable Reduction Cases","authors":"Kento Yamamoto","doi":"10.3836/tjm/1502179342","DOIUrl":"https://doi.org/10.3836/tjm/1502179342","url":null,"abstract":"In this paper, we define a syntomic complex for modulus pair $(X,D)$, where $X$ is a regular semi-stable family and $D$ is an effective Cartier divisor on $X$ and we compute its cohomology sheaves. We construct a symbol map for this syntomic complex for modulus pair $(X,D)$ and investigate its cokernel by computing its cohomology sheaves. To compute the structure of the cohomology sheaves of syntomic complex with modulus, we define some filtrations on it.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43028180","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":"Computation of Some Leafwise Cohomology Ring","authors":"S. Mori","doi":"10.3836/tjm/1502179396","DOIUrl":"https://doi.org/10.3836/tjm/1502179396","url":null,"abstract":"Let $G$ be the group $SL(2,mathbb{R})$, $Psubset G$ be the parabolic subgroup of upper triangular matrices and $Gammasubset G$ be a cocompact lattice. A right action of $P$ on $Gammabackslash G$ defines an orbit foliation $mathcal{F}_P$. We compute the leafwise cohomology ring $H^*(mathcal{F}_P)$ by exploiting non-abelian harmonic analysis on $G$.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48424965","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 Multi-parameter Family of Self-avoiding Walks on the\u0000 Sierpiński Gasket","authors":"T. Otsuka","doi":"10.3836/TJM/1502179338","DOIUrl":"https://doi.org/10.3836/TJM/1502179338","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":"-1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48323683","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}