Mostrando recursos 1 - 20 de 2.306

  1. Degenerate affine Grassmannians and loop quivers

    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...

  2. A remark about weak fillings

    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...

  3. On $81$ symplectic resolutions of a $4$ -dimensional quotient by a group of order $32$

    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...

  4. Endpoint compactness of singular integrals and perturbations of the Cauchy integral

    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.

  5. Cable algebras and rings of $\mathbb{G}_{a}$ -invariants

    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...

  6. Optimal transportation of processes with infinite Kantorovich distance: Independence and symmetry

    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.

  7. Decay structure of two hyperbolic relaxation models with regularity loss

    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...

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

    Freudenburg, Gene

  9. 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...

  10. 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.

  11. 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...

  12. 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.

  13. 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...

  14. 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.

  15. 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.

  16. 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.

  17. 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...

  18. 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.

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

    Kaji, Shizuo

  20. 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...

Aviso de cookies: Usamos cookies propias y de terceros para mejorar nuestros servicios, para análisis estadístico y para mostrarle publicidad. Si continua navegando consideramos que acepta su uso en los términos establecidos en la Política de cookies.