Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
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2024-05-01
Reduction of abelian varieties and curves
Moshe Jarden, Aharon RazonAbstract : Consider a Noetherian domain $R_0$ with quotient field $K_0$. Let $K$ be a finitely generated regular transcendental field extension of $K_0$. We construct a Noetherian domain $R$ with $\mathrm{Quot}(R)=K$ that contains $R_0$ and embed $\mathrm{Spec}(R_0)$ into $\mathrm{Spec}$. Then, we prove that key properties of abelian varieties and smooth geometrically integral projective curves over $K$ are preserved under reduction modulo $\mathfrak{p}$ for ``almost all'' $\mathfrak{p}\in\mathrm{Spec}(R_0)$.
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2024-11-01
Decorated sheaves and morphisms in tilted hearts
Yinbang Lin, Sz-Sheng Wang, Bingyu XiaAbstract : We identify stable pairs and stable framed sheaves as epimorphisms and monomorphisms in the hearts of tilted $t$-structures under appropriate conditions. We then identify the moduli spaces with the corresponding Quot spaces. As a result, we obtain the projectivity of the Quot spaces in absolute cases. In addition, we prove a formula in a motivic Hall algebra, which relates together the Quot spaces under a tilt.
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2024-01-01
Rigidity and nonexistence of Riemannian immersions in semi-Riemannian warped products via parabolicity
Railane Antonia, Henrique de Lima, Márcio SantosAbstract : In this paper, we study complete Riemannian immersions into a semi-Riemannian warped product obeying suitable curvature constraints. Under appropriate differential inequalities involving higher order mean curvatures, we establish rigidity and nonexistence results concerning these immersions. Applications to the cases that the ambient space is either an Einstein manifold, a steady state type spacetime or a pseudo-hyperbolic space are given, and a particular investigation of entire graphs constructed over the fiber of the ambient space is also made. Our approach is based on a parabolicity criterion related to a linearized differential operator which is a divergence-type operator and can be regarded as a natural extension of the standard Laplacian.
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2023-11-01
On the $\eta$-parallelism in almost Kenmotsu $3$-manifolds
Jun-ichi Inoguchi, Ji-Eun LeeAbstract : In this paper, we study the $\eta$-parallelism of the Ricci operator of almost Kenmotsu $3$-manifolds. First, we prove that an almost Kenmotsu $3$-manifold $M$ satisfying $\nabla_{\xi}h=-2\alpha h \varphi$ for some constant $\alpha$ has dominantly $\eta$-parallel Ricci operator if and only if it is locally symmetric. Next, we show that if $M$ is an $H$-almost Kenmotsu $3$-manifold satisfying $\nabla_{\xi}h=-2\alpha h \varphi$ for a constant $\alpha$, then $M$ is a Kenmotsu $3$-manifold or it is locally isomorphic to certain non-unimodular Lie group equipped with a left invariant almost Kenmotsu structure. The dominantly $\eta$-parallelism of the Ricci operator is equivalent to the local symmetry on homogeneous almost Kenmotsu $3$-manifolds.
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2023-11-01
Finite quotients of singular Artin monoids and categorification of the desingularization map
Helena Jonsson, Volodymyr Mazorchuk, Elin Persson Westin, Shraddha Srivastava, Mateusz Stroinski, Xiaoyu ZhuAbstract : We study various aspects of the structure and representation theory of singular Artin monoids. This includes a number of generalizations of the desingularization map and explicit presentations for certain finite quotient monoids of diagrammatic nature. The main result is a categorification of the classical desingularization map for singular Artin monoids associated to finite Weyl groups using BGG category $\mathcal{O}$.
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2023-09-01
Infinite families of congruences modulo $2$ for $2$-core and $13$-core partitions
Ankita Jindal, Nabin Kumar MeherAbstract : A partition of $n$ is called a $t$-core partition if none of its hook number is divisible by $t$. In 2019, Hirschhorn and Sellers [5] obtained a parity result for $3$-core partition function $a_3(n)$. Motivated by this result, both the authors [8] recently proved that for a non-negative integer $\alpha$, $a_{3^{\alpha} m}(n)$ is almost always divisible by an arbitrary power of $2$ and $3$ and $a_{t}(n)$ is almost always divisible by an arbitrary power of $p_i^j$, where $j$ is a fixed positive integer and $t= p_1^{a_1}p_2^{a_2}\cdots p_m^{a_m}$ with primes $p_i \geq 5.$ In this article, by using Hecke eigenform theory, we obtain infinite families of congruences and multiplicative identities for $a_2(n)$ and $a_{13}(n)$ modulo $2$ which generalizes some results of Das [2].
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2024-03-01
Real hypersurfaces in the complex hyperbolic quadric with cyclic parallel structure Jacobi operator
Jin Hong Kim, Hyunjin Lee, Young Jin SuhAbstract : Let $M$ be a real hypersurface in the complex hyperbolic quadric~${Q^{m}}^{*}$, $m \geq 3$. The Riemannian curvature tensor field~$R$ of~$M$ allows us to define a symmetric Jacobi operator with respect to the Reeb vector field~$\xi$, which is called the structure Jacobi operator~$R_{\xi} = R(\, \cdot \, , \xi) \xi \in \text{End}(TM)$. On the other hand, in~\cite{Semm03}, Semmelmann showed that the cyclic parallelism is equivalent to the Killing property regarding any symmetric tensor. Motivated by his result above, in this paper we consider the cyclic parallelism of the structure Jacobi operator~$R_{\xi}$ for a real hypersurface~$M$ in the complex hyperbolic quadric~${Q^{m}}^{*}$. Furthermore, we give a complete classification of Hopf real hypersurfaces in ${Q^{m}}^{*}$ with such a property.
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2024-07-01
Asymptotic behavior for strongly damped wave equations on $\mathbb R^3$ with memory
Xuan-Quang Bui, Duong Toan Nguyen, Trong Luong VuAbstract : We consider the following strongly damped wave equation on $\mathbb{R}^3$ with memory $$ u_{tt} - \alpha \Delta u_{t} - \beta \Delta u +\lambda u - \int_{0}^\infty \kappa'( s) \Delta u(t-s)ds+ f(x,u) +g(x,u_t)=h, $$ where a quite general memory kernel and the nonlinearity $f$ exhibit a critical growth. Existence, uniqueness and continuous dependence results are provided as well as the existence of regular global and exponential attractors of finite fractal dimension.
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2023-11-01
The Bongartz's theorem of Gorenstein cosilting complexes
Hailou Yao, Qianqian YuanAbstract : We describe the Gorenstein derived categories of Gorenstein rings via the homotopy categories of Gorenstein injective modules. We also introduce the concept of Gorenstein cosilting complexes and study its basic properties. This concept is generalized by cosilting complexes in relative homological methods. Furthermore, we investigate the existence of the relative version of the Bongartz's theorem and construct a Bongartz's complement for a Gorenstein precosilting complex.
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2023-09-01
Erratum to ``Pseudo-Riemannian Sasaki solvmanifolds'' [J. Korean Math. Soc. 60 (2023), No. 1, pp. 115--141]
Diego Conti, Federico A. Rossi, Romeo Segnan DalmassoAbstract : In this erratum, we offer a correction to [J. Korean Math. Soc. 60 (2023), No. 1, pp. 115--141]. We rectify Theorem 5.7 and Table 1 of the original paper.
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Unconditional stability and convergence of fully discrete FEM for the viscoelastic Oldroyd flow with an introduced auxiliary variable
Huifang Zhang, Tong Zhang
J. Korean Math. Soc. 2023; 60(2): 273-302
https://doi.org/10.4134/JKMS.j210671 -
Some algebras having relations like those for the 4-dimensional Sklyanin algebras
Alexandru Chirvasitu, S. Paul Smith
J. Korean Math. Soc. 2023; 60(4): 745-777
https://doi.org/10.4134/JKMS.j220200 -
Cup product on relative bounded cohomology
HeeSook Park
J. Korean Math. Soc. 2023; 60(4): 823-833
https://doi.org/10.4134/JKMS.j220345 -
Complete noncompact submanifolds of manifolds with negative curvature
Ya Gao
, Yanling Gao, Jing Mao , Zhiqi XieJ. Korean Math. Soc. 2024; 61(1): 183-205
https://doi.org/10.4134/JKMS.j230283
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On non-displaceable Lagrangian submanifolds in two-step flag varieties
Yoosik Kim
J. Korean Math. Soc. 2023; 60(5): 1109-1133
https://doi.org/10.4134/JKMS.j230098 -
Cup product on relative bounded cohomology
HeeSook Park
J. Korean Math. Soc. 2023; 60(4): 823-833
https://doi.org/10.4134/JKMS.j220345 -
Remarks on Ulrich bundles of small ranks over quartic fourfolds
Yeongrak Kim
J. Korean Math. Soc. 2024; 61(2): 279-291
https://doi.org/10.4134/JKMS.j230104 -
Erratum to ``Pseudo-Riemannian Sasaki solvmanifolds'' [J. Korean Math. Soc. 60 (2023), No. 1, pp. 115--141]
Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso
J. Korean Math. Soc. 2023; 60(5): 1135-1136
https://doi.org/10.4134/JKMS.j230073
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