Mostrando recursos 1 - 20 de 70

  1. A note on families of monogenic number fields

    König, Joachim
    We give a sufficient criterion for specializations of certain families of polynomials to yield monogenic number fields. This generalizes constructions in several earlier papers. As applications we give new infinite families of monogenic number fields for several prescribed Galois groups.

  2. A prime geodesic theorem for higher rank buildings

    Deitmar, Anton; McCallum, Rupert
    We prove a prime geodesic theorem for compact quotients of affine buildings and apply it to get class number asymptotics for global fields of positive characteristic.

  3. The effect of Fenchel-Nielsen coordinates under elementary moves

    Tan, Dong; Liu, Peijia; Liu, Xuewen
    We describe the effect of Fenchel-Nielsen coordinates under elementary move for hyperbolic surfaces with geodesic boundaries, punctures and cone points, which generalize Okai's result for surfaces with geodesic boundaries. The proof relies on the parametrization of the Teichmüller space of surface of type (1,1) or (0,4) as a sub-locus of an algebraic equation in $\mathbf{R}^3$. As an application, we show that the hyperbolic length functions of closed curves are asymptotically piecewise linear functions with respect to the Fenchel Nielsen coordinates in the Teichmüller spaces of surfaces with cone points.

  4. On Terai's conjecture

    Zhang, Xin
    Let $p$ be an odd prime such that $b^r+1=2p^t$, where $r$, $t$ are positive integers and $b \equiv$ 3,5 (mod 8). We show that the Diophantine equation $x^2+b^m=p^n$ has only the positive integer solution $(x,m,n)=(p^t-1,r,2t)$. We also prove that if $b$ is a prime and $r=t=2$, then the above equation has only one solution for the case $b \equiv$ 3,5,7 (mod 8) and the case $d$ is not an odd integer greater than 1 if $b \equiv$ 1 (mod 8), where $d$ is the order of prime divisor of ideal ($p$) in the ideal class group of $\mathbf{Q}$ ($\sqrt {-q}$).

  5. Foxby equivalences associated to strongly Gorenstein modules

    Zhang, Wanru; Liu, Zhongkui; Yang, Xiaoyan
    In order to establish the Foxby equivalences associated to strongly Gorenstein modules, we introduce the notions of strongly $\mathcal{W}_P$-Gorenstein, $\mathcal{W}_I$-Gorenstein and $\mathcal{W}_F$-Gorenstein modules and discuss some basic properties of these modules. We show that the subcategory of strongly Gorenstein projective left $R$-modules in the left Auslander class and the subcategory of strongly $\mathcal{W}_P$-Gorenstein left $S$-modules are equivalent under Foxby equivalence. The injective and flat case are also studied.

  6. Based chord diagrams of spherical curves

    Ito, Noboru
    This paper demonstrates an approach for developing a framework to produce invariants of base-point-free generic spherical curves under some chosen local moves from Reidemeister moves using based chord diagrams. Our invariants not only contain Arnold's classical generic spherical curve invariant but also new invariants.

  7. On the complex Łojasiewicz inequality with parameter

    Denkowski, Maciej P.
    We prove a continuity property in the sense of currents of a continuous family of holomorphic functions which allows us to obtain a Łojasiewicz inequality with an effective exponent independent of the parameter.

  8. Convexity and the Dirichlet problem of translating mean curvature flows

    Ma, Li
    In this work, we propose a new evolving geometric flow (called translating mean curvature flow) for the translating solitons of hypersurfaces in $R^{n+1}$. We study the basic properties, such as positivity preserving property, of the translating mean curvature flow. The Dirichlet problem for the graphical translating mean curvature flow is studied and the global existence of the flow and the convergence property are also considered.

  9. On Perez Del Pozo's lower bound of Weierstrass weight

    Wangyu, Nan; Kawasaki, Masumi; Sakai, Fumio
    Let $V$ be a smooth projective curve over the complex number field with genus $g \geq 2$, and let $\sigma$ be an automorphism on $V$ such that the quotient curve $V/\langle \sigma \rangle$ has genus 0. We write $d$ (resp., $b$) for the order of $\sigma$ (resp., the number of fixed points of $\sigma$). When $d$ and $b$ are fixed, the lower bound of the (Weierstrass) weights of fixed points of $\sigma$ was obtained by Perez del Pozo [7]. We obtain necessary and sufficient conditions for when the lower bound is attained.

  10. Curvature properties of homogeneous real hypersurfaces in nonflat complex space forms

    Maeda, Sadahiro; Tamaru, Hiroshi; Tanabe, Hiromasa
    In this paper, we study curvature properties of all homogeneous real hypersurfaces in nonflat complex space forms, and determine their minimalities and the signs of their sectional curvatures completely. These properties reflect the sign of the constant holomorphic sectional curvature $c$ of the ambient space. Among others, for the case of $c$ < 0 there exist homogeneous real hypersurfaces with positive sectional curvature and also ones with negative sectional curvature, whereas for the case of $c$ > 0 there do not exist any homogeneous real hypersurfaces with nonpositive sectional curvature.

  11. The Hessian of quantized Ding functionals and its asymptotic behavior

    Takahashi, Ryosuke
    We compute the Hessian of quantized Ding functionals and give an elementary proof for the convexity of quantized Ding functionals along Bergman geodesics from the view point of projective geometry. We study also the asymptotic behavior of the Hessian using the Berezin-Toeplitz quantization.

  12. A non-integrated hypersurface defect relation for meromorphic maps over complete Kähler manifolds into projective algebraic varieties

    Chen, Wei; Han, Qi
    In this paper, a non-integrated defect relation for meromorphic maps from complete Kähler manifolds $M$ into smooth projective algebraic varieties $V$ intersecting hypersurfaces located in $k$-subgeneral position (see (1.5) below) is proved. The novelty of this result lies in that both the upper bound and the truncation level of our defect relation depend only on $k$, $\dim_{\,\mathbf{C}}(V)$ and the degrees of the hypersurfaces considered; besides, this defect relation recovers Hirotaka Fujimoto [6, Theorem 1.1] when subjected to the same conditions.

  13. Ultra-discrete equations and tropical counterparts of some complex analysis results

    Chen, Min-Feng; Gao, Zong-Sheng; Zhang, Ji-Long
    A tropical version of Nevanlinna theory describes value distribution of continuous piecewise linear functions of a real variable. In this paper, we present some results on value distribution theory of tropical difference polynomials and uniqueness theory of tropical entire functions. Application to some ultra-discrete equations is also given.

  14. Cyclic coverings of the projective line by Mumford curves in positive characteristic

    Mikami, Ryota
    We study the rigid analytic geometry of cyclic coverings of the projective line. We determine the defining equation of cyclic coverings of degree $p$ of the projective line by Mumford curves over complete discrete valuation fields of positive characteristic $p$. Previously, Bradley studied that of any degree over non-archimedean local fields of characteristic zero.

  15. Zeta functions for Kähler graphs

    Tuerxunmaimaiti, Yaermaimaiti; Adachi, Toshiaki
    To create a discrete analogue of magnetic fields on Riemannian manifolds is a challenging problem. The notion of Kähler graphs introduced by the second author is one of trials of this discretization. In this article we study the asymptotic behavior of the weighted number of prime cycles with respect to their lengths by use of a zeta function.

  16. On complex deformations of Kähler-Ricci solitons

    Pali, Nefton
    We obtain a formal obstruction, i.e. a necessary condition for the existence of polarized complex deformations of Kähler-Ricci solitons. This obstruction is expressed in terms of the harmonic part of the variation of the complex structure.

  17. A regulator map for 1-cycles with modulus

    Onoda, Mirai
    Let $k$ be a field of characteristic 0. We define a map from the additive higher Chow group of 1-cycles with strong sup $m$-modulus $CH_1(A_k(m), n)_{ssup}$ to the module of absolute Kähler differentials of $k$ with twisted $k^*$-action $\Omega^{n-2}_k\langle \omega \rangle$ of weight $\omega$. We will call the map a regulator map, and we show that the regulator map is surjective if $k$ is an algebraically closed field. In case $\omega = m+1$, this map specializes to Park's regulator map. We study a relationship between the cyclic homology and the additive higher Chow group with strong sup modulus by using...

  18. A lower bound for the number of integral solutions of Mordell equation

    Shabani-Solt, Hassan; Janfada, Ali S.
    For a nonzero integer $d$, a celebrated Siegel Theorem says that the number $N(d)$ of integral solutions of Mordell equation $y^2+x^3=d$ is finite. We find a lower bound for $N(d)$, showing that the number of solutions of Mordell equation increases dramatically. We also prove that for any positive integer $n$, there is an integer square multiply represented by Mordell equations, i.e., $k^2=y_1^2+x_1^3=y_2^2+x_2^3=\cdots =y_n^2+x_n^3$.

  19. Generators for the mapping class group of a nonorientable surface

    Hirose, Susumu
    We show that Szepietowski's system of generators for the mapping class group of a non-orientable surface is a minimal generating set by Dehn twists and $Y$-homemorphisms.

  20. Degeneration of period matrices of stable curves

    Yang, Yu
    In the present paper, we study the extent to which linear combinations of period matrices arising from stable curves are degenerate (i.e., as bilinear forms). We give a criterion to determine whether a stable curve admits such a degenerate linear combination of period matrices. In particular, this criterion can be interpreted as a certain analogue of the weight-monodromy conjecture for non-degenerate elements of pro-$\ell$ log étale fundamental groups of certain log points associated to the log stack $\overline{\mathcal{M}}_{g}^{log}$.

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