Recursos de colección
Project Euclid (Hosted at Cornell University Library) (192.977 recursos)
Journal of Mathematics of Kyoto University
Journal of Mathematics of Kyoto University
Feigin, Evgeny; Finkelberg, Michael; Reineke, Markus
We study the connection between the affine degenerate Grassmannians in type $A$ , quiver Grassmannians for one vertex loop quivers, and affine Schubert varieties. We give an explicit description of the degenerate affine Grassmannian of type $\operatorname{GL}_{n}$ and identify it with semi-infinite orbit closure of type $A_{2n-1}$ . We show that principal quiver Grassmannians for the one vertex loop quiver provide finite-dimensional appro- ximations of the degenerate affine Grassmannian. Finally, we give an explicit description of the degenerate affine Grassmannian of type $A_{1}^{(1)}$ , propose a conjectural description in the symplectic case, and discuss the generalization to the case of...
Py, Pierre
Let $L$ be a closed manifold of dimension $n\ge2$ which admits a totally real embedding into $\mathbb{C}^{n}$ . Let $ST^{\ast}L$ be the space of rays of the cotangent bundle $T^{\ast}L$ of $L$ , and let $DT^{\ast}L$ be the unit disk bundle of $T^{\ast}L$ defined by any Riemannian metric on $L$ . We observe that $ST^{\ast}L$ endowed with its standard contact structure admits weak symplectic fillings $W$ which are diffeomorphic to $DT^{\ast}L$ and for which any closed Lagrangian submanifold $N\subset W$ has the property that the map $H_{1}(N,\mathbb{R})\toH_{1}(W,\mathbb{R})$ has a nontrivial kernel. This relies on a variation on a theorem by...
Donten-Bury, Maria; Wiśniewski, Jarosław A.
We provide a construction of $81$ symplectic resolutions of a $4$ -dimensional quotient singularity obtained by an action of a group of order $32$ . The existence of such resolutions is known by a result of Bellamy and Schedler. Our explicit construction is obtained via geometric invariant theory (GIT) quotients of the spectrum of a ring graded in the Picard group generated by the divisors associated to the conjugacy classes of symplectic reflections of the group in question. As a result we infer the geometric structure of these resolutions and their flops. Moreover, we represent the group in question as...
Perfekt, Karl-Mikael; Pott, Sandra; Villarroya, Paco
We prove sufficient and necessary conditions for the compactness of Calderón–Zygmund operators on the endpoint from $L^{\infty}(\mathbb{R})$ into $\mathrm{CMO}(\mathbb{R})$ . We use this result to prove the compactness on $L^{p}(\mathbb{R})$ with $1\lt p\lt \infty$ of a certain perturbation of the Cauchy integral on curves with normal derivatives satisfying a $\mathrm{CMO}$ -condition.
Freudenburg, Gene; Kuroda, Shigeru
For a field $k$ , the ring of invariants of an action of the unipotent $k$ -group $\mathbb{G}_{a}$ on an affine $k$ -variety is quasiaffine, but not generally affine. Cable algebras are introduced as a framework for studying these invariant rings. It is shown that the ring of invariants for the $\mathbb{G}_{a}$ -action on $\mathbb{A}^{5}_{k}$ constructed by Daigle and Freudenburg is a monogenetic cable algebra. A generating cable is constructed for this ring, and a complete set of relations is given as a prime ideal in the infinite polynomial ring over $k$ . In addition, it is shown that the...
Kolesnikov, Alexander V.; Zaev, Danila A.
We consider probability measures on $\mathbb{R}^{\infty}$ and study optimal transportation mappings for the case of infinite Kantorovich distance. Our examples include (1) quasiproduct measures and (2) measures with certain symmetric properties, in particular, exchangeable and stationary measures. We show in the latter case that the existence problem for optimal transportation is closely related to the ergodicity of the target measure. In particular, we prove the existence of the symmetric optimal transportation for a certain class of stationary Gibbs measures.
Ueda, Yoshihiro; Duan, Renjun; Kawashima, Shuichi
This article investigates two types of decay structures for linear symmetric hyperbolic systems with nonsymmetric relaxation. Previously, the same authors introduced a new structural condition which is a generalization of the classical Kawashima–Shizuta condition and also analyzed the weak dissipative structure called the regularity-loss type for general systems with nonsymmetric relaxation, which includes the Timoshenko system and the Euler–Maxwell system as two concrete examples. Inspired by the previous work, we further construct in this article two more complex models which satisfy some new decay structure of regularity-loss type. The proof is based on the elementary Fourier energy method as well...
Freudenburg, Gene
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.
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We also show some relations between those maps and catastrophe theory. The set of the critical values of...
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.
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...
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.
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...
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.
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.
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.
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...
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.
Kaji, Shizuo
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...