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Basic kirwan injectivity and its applications 基本柯万注入性及其应用
IF 0.7 4区 数学 Q3 MATHEMATICS Pub Date : 2022-12-03 DOI: 10.1093/qmath/haac038
Yi Lin, Xiangdong Yang
Consider the Hamiltonian action of a torus on a transversely symplectic foliation that is also Riemannian. When the transverse hard Lefschetz property is satisfied, we establish a foliated version of the Kirwan injectivity theorem and use it to study Hamiltonian torus actions on transversely Kähler foliations. Among other things, we prove a foliated analogue of the Carrell–Liberman theorem. As an application, this confirms a conjecture raised by Battaglia–Zaffran on the basic Hodge numbers of symplectic toric quasifolds. Our methods also allow us to present a symplectic approach to the calculation of the basic Betti numbers of symplectic toric quasifolds.
考虑环面对一个横辛叶理的哈密顿作用,这个叶理也是黎曼的。当横向硬Lefschetz性质满足时,我们建立了Kirwan注入定理的叶状版本,并利用它研究了横向Kähler叶状上的哈密顿环面作用。除此之外,我们证明了Carrell-Liberman定理的叶状类比。作为一个应用,这证实了Battaglia-Zaffran关于辛环拟折叠的基本Hodge数的一个猜想。我们的方法也允许我们提出一种辛方法来计算辛环准折叠的基本Betti数。
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引用次数: 0
On weak compactness in projective tensor products 关于射影张量积的弱紧性
IF 0.7 4区 数学 Q3 MATHEMATICS Pub Date : 2022-11-29 DOI: 10.1093/qmath/haac036
José Rodríguez
We study the property of being strongly weakly compactly generated (and some relatives) in projective tensor products of Banach spaces. Our main result is as follows. Let $1 unicode{x003C} p,qunicode{x003C}infty$ be such that $1/p+1/qgeq 1$. Let X (resp., Y) be a Banach space with a countable unconditional finite-dimensional Schauder decomposition having a disjoint lower p-estimate (resp., q-estimate). If X and Y are strongly weakly compactly generated, then so is their projective tensor product $X {widehat{otimes}_pi} Y$.
研究了Banach空间的射影张量积的强弱紧生成(及其相关性质)。我们的主要结果如下。让$1 unicode{x003C} p,qunicode{x003C}infty$变成$1/p+1/qgeq 1$。设X。, Y)是一个Banach空间,该空间具有一个不相交的低p估计(p < 0.05)的可数无条件有限维Schauder分解。, q-estimate)。如果X和Y是强弱紧生成的,那么它们的射影张量积$X {widehat{otimes}_pi} Y$也是。
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引用次数: 0
Quantifying conjugacy separability in wreath products of groups 群环积共轭可分性的定量化
IF 0.7 4区 数学 Q3 MATHEMATICS Pub Date : 2022-11-25 DOI: 10.1093/qmath/haac031
Michal Ferov, Mark Pengitore
We study generalizations of conjugacy separability in restricted wreath products of groups. We provide an effective upper bound for $mathcal{C}$-conjugacy separability of a wreath product $A wr B$ in terms of the $mathcal{C}$-conjugacy separability of A and B, the growth of $mathcal{C}$-cyclic subgroup separability of B and the $mathcal{C}$-residual girth of $B.$ As an application, we provide a characterization of when $A wr B$ is p-conjugacy separable. We use this characterization to provide for each prime p an example of a wreath product with infinite base group that is p-conjugacy separable. We also provide asymptotic upper bounds for conjugacy separability for wreath products of nilpotent groups, which include the lamplighter groups and provide asymptotic upper bounds for conjugacy separability of the free metabelian groups.
研究了群的受限环积共轭可分性的推广。利用a和B的$mathcal{C}$-共轭可分性、B的$mathcal{C}$-循环子群可分性的增长和$B的$mathcal{C}$-残围,给出环积$ a wr $的$mathcal{C}$-共轭可分性的有效上界。作为应用,我们给出了a wr B$是p共轭可分的一个表征。我们利用这一性质为每个素数p提供了一个具有无限基群的环积是p共轭可分的例子。给出了包括lamplighter群在内的幂零群环积共轭可分性的渐近上界,并给出了自由亚丫群共轭可分性的渐近上界。
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引用次数: 0
Twists of rational Cherednik algebras 有理Cherednik代数的扭曲
IF 0.7 4区 数学 Q3 MATHEMATICS Pub Date : 2022-11-14 DOI: 10.1093/qmath/haac033
Y Bazlov, E Jones-Healey, A Mcgaw, A Berenstein
We show that braided Cherednik algebras introduced by Bazlov and Berenstein are cocycle twists of rational Cherednik algebras of the imprimitive complex reflection groups $G(m,p,n)$, when m is even. This gives a new construction of mystic reflection groups which have Artin–Schelter regular rings of quantum polynomial invariants. As an application of this result, we show that a braided Cherednik algebra has a finite-dimensional representation if and only if its rational counterpart has one.
证明了当m为偶数时,Bazlov和Berenstein引入的辫状Cherednik代数是非原复反射群G(m,p,n)$的有理Cherednik代数的环扭转。给出了具有量子多项式不变量Artin-Schelter正则环的神秘反射群的一种新构造。作为这个结果的一个应用,我们证明了一个编织Cherednik代数有有限维表示当且仅当它的有理对应物有有限维表示。
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引用次数: 0
A Geometric Characterization of the Hjelmslev–Moufang Planes Hjelmslev–Moufang平面的几何特征
IF 0.7 4区 数学 Q3 MATHEMATICS Pub Date : 2021-10-25 DOI: 10.1093/QMATH/HAAB043
A. Schepper, J. Schillewaert, Hendrik Van Maldeghemmagali Victoor, Magali Victoor
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引用次数: 1
Genus 0 Gopakumar–Vafa Invariants of the Banana Manifold 香蕉流形的0 Gopakumar-Vafa不变量属
IF 0.7 4区 数学 Q3 MATHEMATICS Pub Date : 2021-05-19 DOI: 10.1093/QMATH/HAAB026
Nina Morishige
The Banana manifold $X_{{text{Ban}}}$ is a compact Calabi–Yau threefold constructed as the conifold resolution of the fiber product of a generic rational elliptic surface with itself, which was first studied by Bryan. We compute Katz’s genus 0 Gopakumar–Vafa invariants of fiber curve classes on the Banana manifold $X_{{text{Ban}}}to mathbf{P} ^1$. The weak Jacobi form of weight −2 and index 1 is the associated generating function for these genus 0 Gopakumar–Vafa invariants. The invariants are shown to be an actual count of structure sheaves of certain possibly non-reduced genus 0 curves on the universal cover of the singular fibers of $X_{{text{Ban}}}tomathbf{P}^1$.
Banana流形$X_{text{Ban}}$是一个紧的Calabi–Yau三重,由Bryan首次研究,它被构造为具有自身的一般有理椭圆表面的纤维乘积的针叶树分辨率。我们计算Banana流形$X_{text{Ban}} to mathbf{P}^1$上纤维曲线类的Katz亏格0 Gopakumar–Vafa不变量。权重−2和索引1的弱Jacobi形式是这些亏格0 Gopakumar–Vafa不变量的相关生成函数。不变量被证明是$X_{text{Ban}} to mathbf{P}^1$的奇异纤维的泛覆盖上某些可能非约化亏格0曲线的结构簇的实际计数。
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引用次数: 0
Two-Dimensional Locally Nash Groups 二维局部纳什群
IF 0.7 4区 数学 Q3 MATHEMATICS Pub Date : 2021-04-23 DOI: 10.1093/QMATH/HAAB021
E. Baro, J. Vicente, M. Otero
We give a classification of connected abelian locally (real) Nash groups of dimension two. We first consider Painlevé’s description of meromorphic maps admitting an algebraic addition theorem and analyse the algebraic dependence of such maps. We then give a classification of connected abelian locally complex Nash groups of dimension two, from which we deduce the corresponding real classification. As a consequence, we obtain a classification of two-dimensional abelian irreducible algebraic groups defined over $mathbb{R}$.
给出了二维连通阿贝尔局部(实)纳什群的分类。首先考虑painlevel对亚纯映射的代数加法定理的描述,并分析了亚纯映射的代数相关性。然后给出了二维连通阿贝尔局部复纳什群的分类,并由此推导出相应的实分类。因此,我们得到了定义在$mathbb{R}$上的二维阿贝尔不可约代数群的一个分类。
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引用次数: 0
Remarks On Ornstein’s Non-Inequality In ℝ2×2 关于Ornstein在t上的非不等式的注解2×2
IF 0.7 4区 数学 Q3 MATHEMATICS Pub Date : 2021-03-18 DOI: 10.1093/QMATH/HAAB016
D. Faraco, André Guerra
We give a very concise proof of Ornstein’s L1 non-inequality for first- and second-order operators in two dimensions. The proof just needs a two-dimensional laminate supported on three points.
我们给出了二维一阶和二阶算子的Ornstein L1非不等式的一个非常简明的证明。证明只需要一个由三点支撑的二维层压板。
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引用次数: 6
Gradient Estimates of ω-Minimizers to Double Phase Variational Problems with Variable Exponents 变指数双相变分问题的ω-极小值的梯度估计
IF 0.7 4区 数学 Q3 MATHEMATICS Pub Date : 2021-01-19 DOI: 10.1093/QMATH/HAAA067
Sun-Sig Byun, Ho-Sik Lee
We are concerned with an optimal regularity for ω-minimizers to double phase variational problems with variable exponents where the associated energy density is allowed to be discontinuous. We identify basic structure assumptions on the density for the absence of Lavrentiev phenomenon and higher integrability. Moreover, we establish a local Calderón–Zygmund theory for such generalized minimizers under minimal regularity requirements regarding such double phase functionals to the frame of Lebesgue spaces with variable exponents.
我们关注可变指数双相变分问题的ω最小值的最优正则性,其中相关能量密度允许不连续。在没有Lavrentiev现象和较高可积性的情况下,我们确定了密度的基本结构假设。此外,在变指数Lebesgue空间框架下,对于这类双相泛函,我们建立了在极小正则性要求下的广义极小解的局部Calderón-Zygmund理论。
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引用次数: 4
Surjective Homomorphisms from Algebras of Operators on Long Sequence Spaces are Automatically Injective 长序列空间上算子代数的满射同态是自动内射的
IF 0.7 4区 数学 Q3 MATHEMATICS Pub Date : 2021-01-01 DOI: 10.1093/qmath/haaa066
Bence HorvÁth;Tomasz Kania
We study automatic injectivity of surjective algebra homomorphisms from $mathscr{B}(X)$, the algebra of (bounded, linear) operators on X, to $mathscr{B}(Y)$, where X is one of the following long sequence spaces: c0(λ), $ell_{infty}^c(lambda)$, and $ell_p(lambda)$ ($1 leqslant p lt infty$) and Y is arbitrary. En route to the proof that these spaces do indeed enjoy such a property, we classify two-sided ideals of the algebra of operators of any of the aforementioned Banach spaces that are closed with respect to the ‘sequential strong operator topology’.
我们研究了满射代数同态的自动注入性,从$mathscr{B}(X)$,(有界的,线性的)算子在X上的代数,到$mathscr{B}(Y)$,其中X是下列长序列空间之一:c0(λ), $ell_{infty}^c(lambda)$和$ell_p(lambda)$ ($1 leqslant p lt infty$), Y是任意的。在证明这些空间确实具有这样的性质的过程中,我们对任何上述的Banach空间的算子代数的双面理想进行了分类,这些空间相对于“顺序强算子拓扑”是封闭的。
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引用次数: 4
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Quarterly Journal of Mathematics
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