Mostrando recursos 1 - 20 de 55

  1. 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.

  2. 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...

  3. 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., $k^2=y_1^2+x_1^3=y_2^2+x_2^3=\cdots =y_n^2+x_n^3$.

  4. 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.

  5. 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 $\overline{\mathcal{M}}_{g}^{log}$.

  6. Uniqueness theorem for meromorphic mappings with multiple values

    Giang, Ha Huong
    In this article, we will prove a uniqueness theorem for meromorphic mappings into complex projective space $\mathbf{P}^n(\mathbf{C})$ with different multiple values and a general condition on the intersections of the inverse images of these hyperplanes.

  7. Linear Weingarten spacelike hypersurfaces in Lorentz space forms with prescribed Gauss map

    Chao, Xiaoli; Lv, Yusha
    This paper address the geometry of complete linear Weingarten spacelike hypersurfaces in the Lorentz space forms. First, a divergence lemma concerning linear Weingarten spacelike hypersurfaces is obtained. Then, with the aid of this lemma, by supposing suitable restrictions on the Gauss map, we show that such hypersurfaces must be totally umbilical, which are some extension of the recent results of Aquino, Bezerra and Lima [7] and Aquino, Lima and Velásquez [11].

  8. Twisted Alexander polynomials of genus one two-bridge knots

    Tran, Anh T.
    Morifuji [14] computed the twisted Alexander polynomial of twist knots for nonabelian representations. In this paper we compute the twisted Alexander polynomial and Reidemeister torsion of genus one two-bridge knots, a class of knots which includes twist knots. As an application, we give a formula for the Reidemeister torsion of the 3-manifold obtained by $\frac{1}{q}$-Dehn surgery on a genus one two-bridge knot.

  9. An isoperimetric inequality for diffused surfaces

    Menne, Ulrich; Scharrer, Christian
    For general varifolds in Euclidean space, we prove an isoperimetric inequality, adapt the basic theory of generalised weakly differentiable functions, and obtain several Sobolev type inequalities. We thereby intend to facilitate the use of varifold theory in the study of diffused surfaces.

  10. An effective Schmidt's subspace theorem for hypersurfaces in subgeneral position in projective varieties over function fields

    Le, Giang
    We established an effective version of Schmidt's subspace theorem on a smooth projective variety $\mathcal{X}$ over function fields of characteristic zero for hypersurfaces located in $m$-subgeneral position with respect to $\mathcal{X}$.

  11. On 3-dimensional homogeneous generalized $m$-quasi-Einstein manifolds

    Hu, Zejun; Li, Dehe
    In this paper, we show that for 3-dimensional homogeneous manifolds only the space form can carry a proper generalized $m$-quasi-Einstein structure.

  12. Dehn twists on Kauffman bracket skein algebras

    Tsuji, Shunsuke
    We give an explicit formula for the action of the Dehn twist along a simple closed curve in a compact connected oriented surface on the completion of the filtered skein modules of the surface. To do this, we introduce filtrations of the Kauffman bracket skein algebra and the Kauffman bracket skein modules of the surface.

  13. Vanishing of Killing vector fields on compact Finsler manifolds

    Shen, Bin
    In this paper, we define a new Ricci curvature on Finsler manifold named the mean Ricci curvature, which is useful in the study of different symmetric fields on manifolds. By presenting a Bochner type formula of Killing vector fields on general Finsler manifolds, we prove the vanishing theorem of the Killing vector fields on any compact Finsler manifold with a negative mean Ricci curvature. This result involves the vanishing theorem of Killing vector fields in the Riemannian case.

  14. Classification results of quasi Einstein solitons

    Huang, Shu Yau; Wang, Lin Feng
    We classify (ρ,τ)-quasi Einstein solitons with (a,τ)-concurrent vector fields. We also give a necessary and sufficient condition for a submanifold to be a (ρ,τ)-quasi Einstein soliton in a Riemannian manifold equipped with an (a,τ)-concurrent vector field.

  15. Classification results of quasi Einstein solitons

    Huang, Shu Yau; Wang, Lin Feng
    We classify (ρ,τ)-quasi Einstein solitons with (a,τ)-concurrent vector fields. We also give a necessary and sufficient condition for a submanifold to be a (ρ,τ)-quasi Einstein soliton in a Riemannian manifold equipped with an (a,τ)-concurrent vector field.

  16. Classification results of quasi Einstein solitons

    Huang, Shu Yau; Wang, Lin Feng
    We classify $(ρ,τ)$-quasi Einstein solitons with $(a,τ)$-concurrent vector fields. We also give a necessary and sufficient condition for a submanifold to be a $(ρ,τ)$-quasi Einstein soliton in a Riemannian manifold equipped with an $(a,τ)$-concurrent vector field.

  17. The Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one

    Hoshi, Yuichiro; Kinoshita, Ryo; Nakayama, Chikara
    We study the Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one. A consequence of the main results is that the isomorphism class of a certain moduli space of hyperbolic curves of genus one over a sub-p-adic field is completely determined by the isomorphism class of the étale fundamental group of the moduli space over the absolute Galois group of the sub-p-adic field. We also prove related results in absolute anabelian geometry.

  18. The Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one

    Hoshi, Yuichiro; Kinoshita, Ryo; Nakayama, Chikara
    We study the Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one. A consequence of the main results is that the isomorphism class of a certain moduli space of hyperbolic curves of genus one over a sub-p-adic field is completely determined by the isomorphism class of the étale fundamental group of the moduli space over the absolute Galois group of the sub-p-adic field. We also prove related results in absolute anabelian geometry.

  19. The Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one

    Hoshi, Yuichiro; Kinoshita, Ryo; Nakayama, Chikara
    We study the Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one. A consequence of the main results is that the isomorphism class of a certain moduli space of hyperbolic curves of genus one over a sub-$p$-adic field is completely determined by the isomorphism class of the étale fundamental group of the moduli space over the absolute Galois group of the sub-$p$-adic field. We also prove related results in absolute anabelian geometry.

  20. On endomorphisms of hypersurfaces

    Karzhemanov, Ilya
    For any prime p ≥ 5, we show that generic hypersurface Xp $subset$ Pp defined over Q admits a non-trivial rational dominant self-map of degree > 1, defined over $\overline{\mathbb{Q}}$ . A simple arithmetic application of this fact is also given.

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