Mostrando recursos 1 - 20 de 2.299

  1. Erratum for “An affine version of a theorem of Nagata”

    Freudenburg, Gene

  2. Holomorphic endomorphisms of $\mathbb{P}^{3}(\mathbb{C})$ related to a Lie algebra of type $A_{3}$ and catastrophe theory

    Uchimura, Keisuke
    The typical chaotic maps $f(x)=4x(1-x)$ and $g(z)=z^{2}-2$ are well known. Veselov generalized these maps. We consider a class of maps $P_{A_{3}}^{d}$ of those generalized maps, view them as holomorphic endomorphisms of ${\mathbb{P}^{3}}({\mathbb{C}})$ , and make use of methods of complex dynamics in higher dimension developed by Bedford, Fornaess, Jonsson, and Sibony. We determine Julia sets $J_{1},J_{2},J_{3},J_{\Pi}$ and the global forms of external rays. Then we have a foliation of the Julia set $J_{2}$ formed by stable disks that are composed of external rays. ¶ We also show some relations between those maps and catastrophe theory. The set of the critical values of...

  3. The derivative and moment of the generalized Riesz–Nágy–Takács function

    Baek, In-Soo
    We give the characterization of the differentiability and nondifferentiability points of a generalization of the Riesz–Nágy–Takács (RNT) singular function, namely, the generalized RNT (GRNT) singular function. A particular characterization generalizes recent multifractal and metric-number-theoretical results associated with the RNT singular function. Furthermore, we compute the moments of the GRNT singular function.

  4. Hyperbolic span and pseudoconvexity

    Hamano, Sachiko; Shiba, Masakazu; Yamaguchi, Hiroshi
    A planar open Riemann surface $R$ admits the Schiffer span $s(R,\zeta)$ to a point $\zeta\in R$ . M. Shiba showed that an open Riemann surface $R$ of genus one admits the hyperbolic span $\sigma_{H}(R)$ . We establish the variation formulas of $\sigma_{H}(t):=\sigma_{H}(R(t))$ for the deforming open Riemann surface $R(t)$ of genus one with complex parameter $t$ in a disk $\Delta$ of center $0$ , and we show that if the total space $\mathcal{R}=\bigcup_{t\in\Delta}(t,R(t))$ is a two-dimensional Stein manifold, then $\sigma_{H}(t)$ is subharmonic on $\Delta$ . In particular, $\sigma_{H}(t)$ is harmonic on $\Delta$ if and only if $\mathcal{R}$ is biholomorphic to...

  5. Boundary limits of monotone Sobolev functions in Musielak–Orlicz spaces on uniform domains in a metric space

    Ohno, Takao; Shimomura, Tetsu
    Our aim in this article is to deal with boundary limits of monotone Sobolev functions in Musielak–Orlicz spaces on uniform domains in a metric space.

  6. Moduli spaces of bundles over nonprojective K3 surfaces

    Perego, Arvid; Toma, Matei
    We study moduli spaces of sheaves over nonprojective K3 surfaces. More precisely, let $\omega$ be a Kähler class on a K3 surface $S$ , let $r\geq2$ be an integer, and let $v=(r,\xi,a)$ be a Mukai vector on $S$ . We show that if the moduli space $M$ of $\mu_{\omega}$ -stable vector bundles with associated Mukai vector $v$ is compact, then $M$ is an irreducible holomorphic symplectic manifold which is deformation equivalent to a Hilbert scheme of points on a K3 surface. Moreover, we show that there is a Hodge isometry between $v^{\perp}$ and $H^{2}(M,\mathbb{Z})$ and that $M$ is projective if...

  7. Volumes de Fano faibles obtenus par éclatement d’une courbe de $\mathbf{P}^{3}$

    D’Almeida, Jean
    Une variété de Fano faible est une variété admettant un diviseur anticanonique gros et numériquement effectif. On donne une caractérisation des volumes de Fano faibles obtenus par éclatement d’une courbe de $\mathbf{P}^{3}$ . Le résultat est optimal.

  8. Trudinger’s inequality and continuity for Riesz potential of functions in Orlicz spaces of two variable exponents over nondoubling measure spaces

    Kanemori, Sachihiro; Ohno, Takao; Shimomura, Tetsu
    In this article, we consider Trudinger’s inequality and continuity for Riesz potentials of functions in Orlicz spaces of two variable exponents near Sobolev’s exponent over nondoubling metric measure spaces.

  9. On the Cremona contractibility of unions of lines in the plane

    Calabri, Alberto; Ciliberto, Ciro
    We discuss the concept of Cremona contractible plane curves, with a historical account on the development of this subject. Then we classify Cremona contractible unions of $d\geq 12$ lines in the plane.

  10. Homological aspects of the dual Auslander transpose, II

    Tang, Xi; Huang, Zhaoyong
    Let $R$ and $S$ be rings, and let $_{R}\omega_{S}$ be a semidualizing bimodule. We prove that there exists a Morita equivalence between the class of $\infty$ - $\omega$ -cotorsion-free modules and a subclass of the class of $\omega$ -adstatic modules. Also, we establish the relation between the relative homological dimensions of a module $M$ and the corresponding standard homological dimensions of $\operatorname{Hom}(\omega,M)$ . By investigating the properties of the Bass injective dimension of modules (resp., complexes), we get some equivalent characterizations of semitilting modules (resp., Gorenstein Artin algebras). Finally, we obtain a dual version of the Auslander–Bridger approximation theorem. As...

  11. Triangulation extensions of self-homeomorphisms of the real line

    Qi, Yi; Zhong, Yumin
    For every sense-preserving self-homeomorphism of the real axis, Hubbard constructed an extension that is a self-homeomorphism of the upper half-plane by triangulation. It is natural to ask if such extensions of quasisymmetric homeomorphisms of the real axis are all quasiconformal. Furthermore, for what sense-preserving self- homeomorphisms are such extensions David mappings? In this article, a sufficient and necessary condition for such extensions to be quasiconformal and a sufficient condition for such extensions to be David mappings are given.

  12. Erratum: Correction to my paper “Mod 2 cohomology of 2-compact groups of low rank”

    Kaji, Shizuo

  13. Extremal transition and quantum cohomology: Examples of toric degeneration

    Iritani, Hiroshi; Xiao, Jifu
    When a singular projective variety $X_{\mathrm{sing}}$ admits a projective crepant resolution $X_{\mathrm{res}}$ and a smoothing $X_{\mathrm{sm}}$ , we say that $X_{\mathrm{res}}$ and $X_{\mathrm{sm}}$ are related by extremal transition. In this article, we study a relationship between the quantum cohomology of $X_{\mathrm{res}}$ and $X_{\mathrm{sm}}$ in some examples. For $3$ -dimensional conifold transition, a result of Li and Ruan implies that the quantum cohomology of a smoothing $X_{\mathrm{sm}}$ is isomorphic to a certain subquotient of the quantum cohomology of a resolution $X_{\mathrm{res}}$ with the quantum variables of exceptional curves specialized to one. We observe that similar phenomena happen for toric degenerations of...

  14. Higher homotopy associativity of power maps on finite $H$ -spaces

    Kawamoto, Yusuke
    Let $p$ be an odd prime, and let $\lambda\in\mathbb{Z}$ . Consider the loop space $Y_{t}=S^{2t-1}_{(p)}$ for $t\ge1$ with $t|(p-1)$ . Then we first determine the condition for the power map $\varPhi_{\lambda}$ on $Y_{t}$ to be an $A_{p}$ -map. We next assume that $X$ is a simply connected $\mathbb{F}_{p}$ -finite $A_{p}$ -space and that $\lambda$ is a primitive $(p-1)$ st root of unity mod $p$ . Our results show that if the reduced power operations $\{\mathscr{P}^{i}\}_{i\ge1}$ act trivially on the indecomposable module $QH^{*}(X;\mathbb{F}_{p})$ and the power map $\varPhi_{\lambda}$ on $X$ is an $A_{n}$ -map with $n\gt (p-1)/2$ , then $X$ is...

  15. Boundedness for fractional Hardy-type operator on variable-exponent Herz–Morrey spaces

    Wu, Jiang-Long; Zhao, Wen-Jiao
    In this article, the fractional Hardy-type operator of variable order $\beta(x)$ is shown to be bounded from the variable-exponent Herz–Morrey spaces $M\dot{K}_{p_{{1}},q_{{1}}(\cdot)}^{\alpha(\cdot),\lambda}(\mathbb{R}^{n})$ into the weighted space $M\dot{K}_{p_{{2}},q_{{2}}(\cdot)}^{\alpha(\cdot),\lambda}(\mathbb{R}^{n},\omega)$ , where $\alpha(x)\in L^{\infty}(\mathbb{R}^{n})$ is log-Hölder continuous both at the origin and at infinity, $\omega=(1+|x|)^{-\gamma(x)}$ with some $\gamma(x)\gt 0$ , and $1/q_{{1}}(x)-1/q_{{2}}(x)=\beta(x)/n$ when $q_{{1}}(x)$ is not necessarily constant at infinity.

  16. Construction of class fields over cyclotomic fields

    Koo, Ja Kyung; Yoon, Dong Sung
    Let $\ell$ and $p$ be odd primes. For a positive integer $\mu$ , let $k_{\mu}$ be the ray class field of $k=\mathbb{Q}(e^{2\pi i/\ell})$ modulo $2p^{\mu}$ . We present certain class fields $K_{\mu}$ of $k$ such that $k_{\mu}\subset K_{\mu}\subset k_{\mu+1}$ , and we provide a necessary and sufficient condition for $K_{\mu}=k_{\mu+1}$ . We also construct, in the sense of Hilbert, primitive generators of the field $K_{\mu}$ over $k_{\mu}$ by using Shimura’s reciprocity law and special values of theta constants.

  17. When do Foxby classes coincide with the classes of modules of finite Gorenstein dimensions?

    Bennis, Driss; García Rozas, J. R.; Oyonarte, Luis
    The relation between the Auslander (resp., Bass) class and the class of modules with finite Gorenstein projective (resp., injective) dimension is well known when these mentioned classes are built with a dualizing module over Noetherian $n$ -perfect rings. Basically, the results are necessary conditions to ensure that both classes coincide. In this article we try to extend and sometimes improve some of these results by weakening the condition of being dualizing. Among other results, we prove that a Wakamatsu tilting module with some extra conditions is precisely a module $_{R}C$ such that the Bass class $\mathcal{B}_{C}(R)$ coincides with the class...

  18. On the $\ell$ -adic cohomology of Jacobian elliptic surfaces over finite fields

    Welters, Gerald E.
    For a Jacobian elliptic surface $S_{0}$ over a finite field $k$ and a prime $\ell$ different from the characteristic of $k$ , the points of period $\ell^{r}$ on the smooth fibers of $S_{0}$ yield, for each $r\in \mathbb{Z}_{\geq 0}$ , a smooth projective curve $C_{r}$ over $k$ by taking Zariski closure in $S_{0}$ and normalization. We consider the restriction map in $\ell$ -adic étale cohomology $H^{2}(S_{0},\mathbb{Z}_{\ell}(1))\rightarrow H^{2}(\bigsqcup _{r\geq 0}C_{r},\mathbb{Z}_{\ell}(1))=\prod_{r\geq 0}H^{2}(C_{r},\mathbb{Z}_{\ell}(1))$ . By using an earlier result of ours we prove that, except for at most a finite number of such primes $\ell$ , this map is faithful on the submodule...

  19. Artin’s conjecture for abelian varieties

    Virdol, Cristian
    Consider $A$ an abelian variety of dimension $r$ defined over $\mathbb{Q}$ . Assume that $\operatorname{rank}_{\mathbb{Q}}A\geq g$ , where $g\geq0$ is an integer, and let $a_{1},\ldots,a_{g}\in A(\mathbb{Q})$ be linearly independent points. (So, in particular, $a_{1},\ldots,a_{g}$ have infinite order, and if $g=0$ , then the set $\{a_{1},\ldots,a_{g}\}$ is empty.) For $p$ a rational prime of good reduction for $A$ , let $\bar{A}$ be the reduction of $A$ at $p$ , let $\bar{a}_{i}$ for $i=1,\ldots,g$ be the reduction of $a_{i}$ (modulo $p$ ), and let $\langle\bar{a}_{1},\ldots,\bar{a}_{g}\rangle$ be the subgroup of $\bar{A}(\mathbb{F}_{p})$ generated by $\bar{a}_{1},\ldots,\bar{a}_{g}$ . Assume that $\mathbb{Q}(A[2])=\mathbb{Q}$ and $\mathbb{Q}(A[2],2^{-1}a_{1},\ldots,2^{-1}a_{g})\neq\mathbb{Q}$ . (Note that...

  20. t-Structures on elliptic fibrations

    Lo, Jason
    We consider t-structures that naturally arise on elliptic fibrations. By filtering the category of coherent sheaves on an elliptic fibration using the torsion pairs corresponding to these t-structures, we prove results describing equivalences of t-structures under Fourier–Mukai transforms.

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