Kodai Mathematical Journal
Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991
Volume 45, Issue 1
Displaying 1-10 of 10 articles from this issue
  • Yoshiaki Fukuma
    2022 Volume 45 Issue 1 Pages 1-18
    Published: March 18, 2022
    Released on J-STAGE: March 18, 2022
    JOURNAL RESTRICTED ACCESS

    Let X denote a smooth projective variety of dimension n defined over the field of complex numbers such that the anti-canonical line bundle -KX of X is nef and big with h0(-KX) > 0, and let L be a nef and big line bundle on X. In this paper, we consider the dimension of the global sections of KX + mL with mn - 1 for this case. In particular, under the assumption that KX + (n - 1)L is nef, we prove that h0(KX + (n - 1)L) > 0 if 6 ≤ n ≤ 9 and L is ample.

    Download PDF (118K)
  • L. V. Dai, N. T. Dung, N. D. Tuyen, L. Zhao
    2022 Volume 45 Issue 1 Pages 19-37
    Published: March 18, 2022
    Released on J-STAGE: March 18, 2022
    JOURNAL RESTRICTED ACCESS

    In this paper, we consider the non-linear general p-Laplacian equation Δp,fu + F(u) = 0 for a smooth function F on smooth metric measure spaces. Assume that a Sobolev inequality holds true on M and an integral Ricci curvature is small, we first prove a local gradient estimate for the equation. Then, as its applications, we prove several Liouville type results on manifolds with lower bounds of Ricci curvature. We also derive new local gradient estimates provided that the integral Ricci curvature is small enough.

    Download PDF (141K)
  • Shota Tsujimura
    2022 Volume 45 Issue 1 Pages 38-48
    Published: March 18, 2022
    Released on J-STAGE: March 18, 2022
    JOURNAL RESTRICTED ACCESS

    In an author's joint work with Hoshi and Mochizuki, we introduced the notion of TKND-AVKF-field [concerning the divisible subgroups of the groups of rational points of semi-abelian varieties] and obtained an anabelian Grothendieck Conjecture-type result for higher dimensional configuration spaces associated to hyperbolic curves over TKND-AVKF-fields. On the other hand, every concrete example of TKND-AVKF-field that appears in this joint work is a ×μ-indivisible field [i.e., a field such that any divisible element of the multiplicative group of the field is a root of unity]. In the present paper, we construct new examples of TKND-AVKF-fields that are not ×μ-indivisible.

    Download PDF (89K)
  • Yoshiyasu Ozeki, Yuichiro Taguchi
    2022 Volume 45 Issue 1 Pages 49-64
    Published: March 18, 2022
    Released on J-STAGE: March 18, 2022
    JOURNAL RESTRICTED ACCESS

    We introduce a notion of highly Kummer-faithful fields and study its relationship with the notion of Kummer-faithful fields. We also give some examples of highly Kummer-faithful fields. For example, if k is a number field of finite degree over , g is an integer > 0 and m = (mp)p is a family of non-negative integers, where p ranges over all prime numbers, then the extension field kg,m obtained by adjoining to k all coordinates of the elements of the pmp-torsion subgroup A[pmp] of A for all semi-abelian varieties A over k of dimension at most g and all prime numbers p, is highly Kummer-faithful.

    Download PDF (143K)
  • Shinpei Sakane, Miho Aoki
    2022 Volume 45 Issue 1 Pages 65-95
    Published: March 18, 2022
    Released on J-STAGE: March 18, 2022
    JOURNAL RESTRICTED ACCESS

    Let x be a complex number which has a positive real part, and w1, ..., wN be positive rational numbers. We show that ws ζN(s, x|w1, ..., wN) can be expressed as a finite linear combination of the Hurwitz zeta functions over Q(x), where ζN(s,x|w1, ..., wN) is the Barnes zeta function and w is a positive rational number explicitly determined by w1, ..., wN. Furthermore, we give generalizations of Kummer's formula on the gamma function and Koyama-Kurokawa's formulae on the multiple gamma functions, and an explicit formula for the values at non-positive integers for higher order derivatives of the Barnes zeta function in the case that x is a positive rational number, involving the generalized Stieltjes constants and the values at positive integers of the Riemann zeta function. Our formulae also makes it possible to calculate an approximation in the case that w1, ..., wN and x are positive real numbers.

    Download PDF (629K)
  • Xuenan Fu, Jia-Yong Wu
    2022 Volume 45 Issue 1 Pages 96-109
    Published: March 18, 2022
    Released on J-STAGE: March 18, 2022
    JOURNAL RESTRICTED ACCESS

    In this paper, we prove Souplet-Zhang type gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces with the compact boundary under the Dirichlet boundary condition when the Bakry-Emery Ricci tensor and the weighted mean curvature are both bounded below. As an application, we obtain a new Liouville type result for some space-time functions on such smooth metric measure spaces. These results generalize previous linear equations to a nonlinear case.

    Download PDF (101K)
  • Takayuki Morifuji
    2022 Volume 45 Issue 1 Pages 110-116
    Published: March 18, 2022
    Released on J-STAGE: March 18, 2022
    JOURNAL RESTRICTED ACCESS

    Dunfield, Friedl and Jackson make a conjecture that the hyperbolic torsion polynomial determines the genus and fibering of hyperbolic knots. In this paper, we study a similar problem for the adjoint torsion polynomial, and show that it determines the genus and fibering of a large family of hyperbolic genus one two-bridge knots.

    Download PDF (97K)
  • Martha P. Dussan, Nikos Georgiou, Martin Magid
    2022 Volume 45 Issue 1 Pages 117-142
    Published: March 18, 2022
    Released on J-STAGE: March 18, 2022
    JOURNAL RESTRICTED ACCESS

    We investigate minimal surfaces in products of two-spheres Sp2×Sp2, with the neutral metric given by (g,-g). Here Sp2Rp,3-p, and g is the induced metric on the sphere. We compute all totally geodesic surfaces and we give a relation between minimal surfaces and the solutions of the Gordon equations. Finally, in some cases we give a topological classification of compact minimal surfaces.

    Download PDF (195K)
  • Xin Xiong, Lingzhong Zeng, Huihui Zhu
    2022 Volume 45 Issue 1 Pages 143-156
    Published: March 18, 2022
    Released on J-STAGE: March 18, 2022
    JOURNAL RESTRICTED ACCESS

    In this paper, we investigate the eigenvalues of the drifting Laplacian on the bounded domain in Hardamard manifolds. By using upper half-plane model, we establish a universal inequality for the drifting Laplacian with a specific class of potential functions on the hyperbolic space, which can be viewed as a rigidity result associated with such a class of functions. Furthermore, we consider general Hardamard manifolds with pinching condition of sectional curvature, and obtain an eigenvalue inequality without the condition of Bakry-Émery curvature. As a by-product, we obtain a universal bound for the case of radial drifting Laplacian satisfying certain growth condition along with the radial direction.

    Download PDF (108K)
  • Taiki Takatsu
    2022 Volume 45 Issue 1 Pages 157-173
    Published: March 18, 2022
    Released on J-STAGE: March 18, 2022
    JOURNAL RESTRICTED ACCESS

    We give a construction of singular K3 surfaces with discriminant 3 and 4 as double coverings over the projective plane. Focusing on the similarities in their branching loci, we can generalize this construction, and obtain a three dimensional moduli space of certain K3 surfaces which admit infinite automorphism groups. Moreover, we show that these K3 surfaces are characterized in terms of the configuration of the singular fibres of a jacobian elliptic fibration and also in terms of periods.

    Download PDF (264K)
feedback
Top