Transformation Groups最新文献

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Factorial Affine $$G_a$$ -Varieties with Height One Plinth Ideals 具有高度为一的基座理想的因子仿射 $$G_a$$ 变体

IF 0.7 3区数学 Q4 MATHEMATICS

Transformation Groups

Pub Date : 2023-12-16 DOI: 10.1007/s00031-023-09833-0

Kayo Masuda

Let (X={text {Spec}};B) be a factorial affine variety defined over an algebraically closed field k of characteristic zero with a nontrivial action of the additive group (G_a) associated to a locally nilpotent derivation (delta ) on B. In this article, we study X of dimension (ge 3) under the assumption that the plinth ideal (text {pl}(delta )=delta (B)cap A) is contained in an ideal (alpha A) generated by a prime element (alpha in A={text {Ker}},delta ). Suppose that (A={text {Ker}},delta ) is an affine k-domain. The quotient morphism (pi : X rightarrow Y={text {Spec}};A) splits to a composite (textrm{pr} circ p) of the projection (textrm{pr}: Ytimes mathbb A^1 rightarrow Y) and a (G_a)-equivariant birational morphism (p: X rightarrow Ytimes mathbb A^1) where (G_a) acts on (mathbb A^1) by translation. By decomposing (p: X rightarrow Ytimes mathbb A^1) to a sequence of (G_a)-equivariant affine modifications, we investigate the structure of X. We also show that the general closed fiber of (pi ) over the closed set (V(alpha )={text {Spec}};A/alpha A) consists of a disjoint union of m affine lines where (mge 2).

让 (X={text {Spec}};B) 是一个定义在特征为零的代数闭域 k 上的因子仿射综，它具有与 B 上的局部零势派生相关联的加法群 (G_a) 的非琐作用。在本文中，我们将研究维数为 (ge 3) 的 X，假设柱顶理想 (text {pl}(delta )=delta (B)cap A) 包含在由素元 (alpha in A={text {Ker}},delta ) 生成的理想 (alpha A) 中。假设 (A={text {Ker},delta) 是一个仿射 k 域。商变形 (pi : X rightarrow Y={text {Spec}};A) 分裂为投影 (textrm{pr} circ p) 的复合 (textrm{pr} circ p)：Ytimes mathbb A^1 rightarrow Y) 和一个 (G_a)-equivariant 双向变形 (p: X rightarrow Ytimes mathbb A^1) 其中 (G_a) 通过平移作用于 (mathbb A^1).通过将 (p: X rightarrow Ytimes mathbb A^1)分解为一系列 (G_a)-equivariant affine modifications，我们研究了 X 的结构。我们还证明了在(V(alpha )={text {Spec}};A/alpha A) 上的闭集(V(alpha )={text {Spec}};A/alpha A) 上的(pi )的一般闭纤维由m条仿射线（其中(mge 2).

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引用次数: 0

Galois Closure of a Fivefold Covering and Decomposition of Its Jacobian 五重覆盖的伽罗瓦封闭及其雅各比分解

IF 0.7 3区数学 Q4 MATHEMATICS

Transformation Groups

Pub Date : 2023-12-13 DOI: 10.1007/s00031-023-09827-y

Benjamín M. Moraga

For an arbitrary fivefold ramified covering (varvec{f :Xrightarrow Y}) between compact Riemann surfaces, each possible Galois closure (varvec{hat{f}:hat{X}rightarrow Y}) is determined in terms of the branching data of (varvec{f}). Since (varvec{{{,textrm{Mon},}}(f)}) acts on (varvec{hat{f}}), it also acts on the Jacobian variety (varvec{{{,textrm{J},}}(X)}), and we describe its group algebra decomposition in terms of the Jacobian and Prym varieties of the intermediate coverings of (varvec{hat{f}}). The dimension and induced polarization of each abelian variety in the decomposition is computed in terms of the branching data of (varvec{f}).

对于紧致黎曼曲面之间的任意五重分支覆盖(varvec{f :Xrightarrow Y})，每个可能的伽罗瓦闭包(varvec{hat{f}:hat{X}rightarrow Y})都是根据(varvec{f})的分支数据确定的。由于(varvec{{{,textrm{Mon},}}(f)})作用于(varvec{hat{f}})，它也作用于雅可比变换(varvec{{{,textrm{J},}}(X)})，我们用(varvec{hat{f}})的中间覆盖的雅可比变换和Prym变换来描述它的群代数分解。利用(varvec{f})的分支数据计算了分解过程中各阿贝尔变量的维数和诱导极化。

引用次数: 0

Compact Hyperbolic Coxeter Five-Dimensional Polytopes with Nine Facets 具有九个面的紧凑双曲考斯特五维多边形

IF 0.7 3区数学 Q4 MATHEMATICS

Transformation Groups

Pub Date : 2023-12-11 DOI: 10.1007/s00031-023-09830-3

Jiming Ma, Fangting Zheng

In this paper, we obtain a complete classification of compact hyperbolic Coxeter five-dimensional polytopes with nine facets.

在本文中，我们获得了具有九个面的紧凑双曲考斯特五维多面体的完整分类。

引用次数: 0

The Limit Set for Representations of Discrete Subgroups of $$text {PU}(1,n)$$ by the Plücker Embedding plicker嵌入表示$$text {PU}(1,n)$$离散子群的极限集

IF 0.7 3区数学 Q4 MATHEMATICS

Transformation Groups

Pub Date : 2023-12-02 DOI: 10.1007/s00031-023-09829-w

Haremy Zuñiga

Let (Gamma ) be a discrete subgroup of (text {PU}(1,n)). In this work, we look at the induced action of (Gamma ) on the projective space (mathbb {P}(wedge ^{k+1}mathbb {C}^{n+1})) by the Plücker embedding, where (wedge ^{k+1}) denotes the exterior power. We define a limit set for this action called the k-Chen-Greenberg limit set, which extends the classical definition of the Chen-Greenberg limit set (L(Gamma )), and we show several of its properties. We prove that its Kulkarni limit set is the union taken over all (pin L(Gamma )) of the projective subspace generated by all k-planes that contain p or are contained in (p^{perp }) via the Plücker embedding. We also prove a duality between both limit sets.

设(Gamma )为(text {PU}(1,n))的离散子群。在这项工作中，我们通过plicker嵌入来研究(Gamma )对投影空间(mathbb {P}(wedge ^{k+1}mathbb {C}^{n+1}))的诱导作用，其中(wedge ^{k+1})表示外部功率。我们为这个动作定义了一个极限集，称为k-Chen-Greenberg极限集，它扩展了Chen-Greenberg极限集的经典定义(L(Gamma ))，并展示了它的几个性质。我们证明了它的Kulkarni极限集是由包含p或包含在(p^{perp })中的所有k-平面生成的射影子空间的所有(pin L(Gamma ))的并集。我们还证明了两个极限集之间的对偶性。

引用次数: 0

Which Schubert Varieties are Hessenberg Varieties? 哪些舒伯特品种是海森伯格品种?

IF 0.7 3区数学 Q4 MATHEMATICS

Transformation Groups

Pub Date : 2023-11-18 DOI: 10.1007/s00031-023-09825-0

Laura Escobar, Martha Precup, John Shareshian

After proving that every Schubert variety in the full flag variety of a complex reductive group G is a general Hessenberg variety, we show that not all such Schubert varieties are adjoint Hessenberg varieties. In fact, in types A and C, we provide pattern avoidance criteria implying that the proportion of Schubert varieties that are adjoint Hessenberg varieties approaches zero as the rank of G increases. We show also that in type A, some Schubert varieties are not isomorphic to any adjoint Hessenberg variety.

在证明复约群G的满旗变种中的每一个Schubert变种都是一般的Hessenberg变种之后，我们证明了并非所有这样的Schubert变种都是伴随Hessenberg变种。事实上，在A和C类型中，我们提供了模式回避准则，暗示随着G的增加，Schubert品种是伴随的Hessenberg品种的比例趋于零。我们还证明了在A型中，一些Schubert变种与任何伴随的Hessenberg变种不同构。

引用次数: 3

On the Invariant and Anti-Invariant Cohomologies of Hypercomplex Manifolds 关于超复流形的不变与反不变上同调

IF 0.7 3区数学 Q4 MATHEMATICS

Transformation Groups

Pub Date : 2023-11-17 DOI: 10.1007/s00031-023-09828-x

Mehdi Lejmi, Nicoletta Tardini

A hypercomplex structure (I, J, K) on a manifold M is said to be (C^infty )-pure-and-full if the Dolbeault cohomology (H^{2,0}_{partial }(M,I)) is the direct sum of two natural subgroups called the (overline{J})-invariant and the (overline{J})-anti-invariant subgroups. We prove that a compact hypercomplex manifold that satisfies the quaternionic version of the (dd^c)-Lemma is (C^infty )-pure-and-full. Moreover, we study the dimensions of the (overline{J})-invariant and the (overline{J})-anti-invariant subgroups, together with their analogue in the Bott-Chern cohomology. For instance, in real dimension 8, we characterize the existence of hyperkähler with torsion metrics in terms of the dimension of the (overline{J})-invariant subgroup. We also study the existence of special hypercomplex structures on almost abelian solvmanifolds.

如果Dolbeault上同调(H^{2,0}_{partial }(M,I))是称为(overline{J}) -不变子群和(overline{J}) -反不变子群的两个自然子群的直接和，则流形M上的超复结构(I, J, K)被称为(C^infty ) -纯满结构。证明了满足(dd^c) -引理四元数形式的紧超复流形是(C^infty ) -纯满的。此外，我们还研究了(overline{J}) -不变子群和(overline{J}) -反不变子群的维数，以及它们在bot - chern上同调中的类似情形。例如，在实维8中，我们用(overline{J})不变子群的维数来表征具有扭转度量的hyperkähler的存在性。研究了概阿贝尔解流形上特殊超复结构的存在性。

引用次数: 0

ON THE BRUHAT $$ mathcal{G} $$-ORDER BETWEEN LOCAL SYSTEMS ON THE B-ORBITS IN A HERMITIAN SYMMETRIC VARIETY 关于厄米对称变化中b轨道上局部系统之间的BRUHAT $$ mathcal{G} $$序

3区数学 Q4 MATHEMATICS

Transformation Groups

Pub Date : 2023-09-23 DOI: 10.1007/s00031-023-09824-1

Michele Carmassi

引用次数: 0

A Moment Map for Twisted-Hamiltonian Vector Fields on Locally Conformally Kähler Manifolds 局部共形Kähler流形上扭曲哈密顿向量场的矩映射

3区数学 Q4 MATHEMATICS

Transformation Groups

Pub Date : 2023-09-20 DOI: 10.1007/s00031-023-09815-2

Daniele Angella, Simone Calamai, Francesco Pediconi, Cristiano Spotti

Abstract We extend the classical Donaldson-Fujiki interpretation of the scalar curvature as moment map in Kähler geometry to the wider framework of locally conformally Kähler geometry.

摘要将Kähler几何中标量曲率作为矩映射的经典Donaldson-Fujiki解释推广到更广泛的局部共形Kähler几何框架中。

引用次数: 0

Centralizers of Nilpotent Elements in Basic Classical Lie Superalgebras in Good Characteristic 基本经典李超代数中幂零元的中心中心

3区数学 Q4 MATHEMATICS

Transformation Groups

Pub Date : 2023-09-12 DOI: 10.1007/s00031-023-09814-3

Leyu Han

Abstract Let $$mathfrak {g}=mathfrak {g}_{bar{0}}oplus mathfrak {g}_{bar{1}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>g</mml:mi> <mml:mover> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> <mml:mo>⊕</mml:mo> <mml:msub> <mml:mi>g</mml:mi> <mml:mover> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> </mml:mrow> </mml:math> be a basic classical Lie superalgebra over an algebraically closed field $$mathbb {K}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>K</mml:mi> </mml:math> whose characteristic $$p>0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> is a good prime for $$mathfrak {g}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>g</mml:mi> </mml:math> . Let $$G_{bar{0}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:mover> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> </mml:math> be the reductive algebraic group over $$mathbb {K}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>K</mml:mi> </mml:math> such that $$textrm{Lie}(G_{bar{0}})=mathfrak {g}_{bar{0}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>Lie</mml:mtext> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>G</mml:mi> <mml:mover> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>g</mml:mi> <mml:mover> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> </mml:mrow> </mml:math> . Suppose $$ein mathfrak {g}_{bar{0}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>e</mml:mi> <mml:mo>∈</mml:mo> <mml:msub> <mml:mi>g</mml:mi> <mml:mover> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> </mml:mrow> </mml:math> is nilpotent. Write $$mathfrak {g}^{e}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mi>e</mml:mi> </mml:msup> </mml:math> for the centralizer of e in $$mathfrak {g}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>g</mml:mi> </mml:math> and $$mathfrak {z}(mathfrak {g}^{e})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mi>e</mml:mi> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> for the centre of $$mathfrak {g}^{e}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mm

设$$mathfrak {g}=mathfrak {g}_{bar{0}}oplus mathfrak {g}_{bar{1}}$$ g = g 0¯⊕g 1¯是代数闭场$$mathbb {K}$$ K上的一个基本经典李超代数，其特征为$$p>0$$ p ＆gt;0是$$mathfrak {g}$$ g的好质数。设$$G_{bar{0}}$$ G 0¯为$$mathbb {K}$$ K上的约化代数群，使得$$textrm{Lie}(G_{bar{0}})=mathfrak {g}_{bar{0}}$$ Lie (G 0¯)= G 0¯。假设$$ein mathfrak {g}_{bar{0}}$$ e∈g 0¯是幂零的。将$$mathfrak {g}$$ g中的e的扶正器写成$$mathfrak {g}^{e}$$ g e，将$$mathfrak {g}^{e}$$ g e的中心写成$$mathfrak {z}(mathfrak {g}^{e})$$ z (g e)。我们通过使用相关的协字符$$tau :mathbb {K}^{times }rightarrow G_{bar{0}}$$ τ: K x→g 0¯(e)来计算$$mathfrak {g}^{e}$$ g e和$$mathfrak {z}(mathfrak {g}^{e})$$ z (g e)的基。此外，我们给出了例外李超代数$$D(2,1;alpha )$$ D (2,1; α)、G(3)和F(4)的可达、强可达或满足Panyushev性质e的分类。

引用次数: 0

Compactifications of Moduli of G-Bundles and Conformal Blocks g束和共形块模的紧化

3区数学 Q4 MATHEMATICS

Transformation Groups

Pub Date : 2023-09-09 DOI: 10.1007/s00031-023-09820-5

Avery Wilson

引用次数: 0

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