Claudio Bartocci, Ugo Bruzzo, Valeriano Lanza, Claudio L. S. Rava
We prove that certain quiver varieties are irreducible and therefore are isomorphic to Hilbert schemes of points of the total spaces of the bundles $\mathcal O_{\mathbb P^1}(-n)$ for $n \ge 1$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We introduce a framework of translation quiver varieties which includes Nakajima quiver varieties as well as their graded and cyclic versions. An important feature of translation quiver varieties is that the sets of their fixed points under toric actions can be again realized as translation quiver varieties. This allows one to simplify quiver varieties in several steps. We prove that translation quiver varieties are smooth, pure and have Tate motivic classes. We also describe an algorithm to compute those motivic classes.
Desingularizations of quiver Grassmannians via graded quiver varieties
灵感最近的工作Cerulli-Feigin-Reineke对desingularizations的Grassmannian的Dynkin箭图表示，我们得到desingularizations在相当更一般的情况下，特别是Grassmannian的模块在迭代倾斜代数Dynkin型。我们的desingularization地图构建从Nakajima的desingularization地图的分等级品种。
In this paper, we introduce generalized quiver varieties which include as special cases classical and cyclic quiver varieties. The geometry of generalized quiver varieties is governed by a finitely generated algebra P: the algebra P is self-injective if the quiver Q is of Dynkin type, and coincides with the preprojective algebra in the case of classical quiver varieties. We show that in the Dynkin case the strata of generalized quiver varieties are in bijection with the isomorphism classes of objects in proj P, and that their degeneration order coincides with the Jensen-Su-Zimmermann's degener…
We unify aspects of the equivariant geometry of type $D$ quiver representation varieties, double Grassmannians, and symmetric varieties $GL(a+b)/GL(a)\times GL(b)$; in particular we translate results about singularities of orbit closures, combinatorics of orbit closure containment, and torus equivariant $K$-theory between these three families. These results are all obtained from our generalization of a construction of Zelevinsky for type $A$ quivers to the type $D$ setting. More precisely, we give explicit embeddings with nice properties of homogeneous fiber bundles over type $D$ quiver repres…
Hilbert irreducibility for abelian varieties over function fields of characteristic zero
该研究证明了特征零函数域上阿贝尔簇的希尔伯特不可约定理，完善了相关数论与代数几何理论。
Quiver varieties and Beilinson-Drinfeld Grassmannians of type A
我们构造Nakajima的A型的共轭类的矩阵和（非Slodowy的）横切片自然产生的仿射格拉斯曼。在完全一般性的情况下，A型的Beilinson-Drinfeld Grassmannian变种嵌入其中。我们的建设提供了一个紧化的Nakajima的Nakajima品种和分解的仿射格拉斯曼到一个不相交的联盟nakajima品种。作为一个应用，我们提供了一个几何版本的斜对称$(GL(m), GL(n))$对偶。
A mixed fibration theorem for Hilbert irreducibility on non-proper varieties
本文证明了在适当条件下，弱希尔伯特性质沿定义在任意特征为零的域上的变种的映射上升。
Coherent Sheaves on Quiver Varieties and Categorification
构造了Nakajima簇上凝聚层的导出范畴上的几何范畴李代数作用。这些行动分类Nakajima的建设卡茨-穆迪代数表示的K-理论上的K-簇。我们在这些导出范畴上定义了一个诱导仿射辫群作用。
On quiver varieties and affine Grassmannians of type A
本文利用A型仿射格拉斯曼簇构造了A型Nakajima簇。这给出了一个紧化的类簇和一个分解的仿射格拉斯曼到一个不相交的联盟类簇。因此，在A型中，仿射簇、幂零轨道和仿射格拉斯曼算子的奇异性是相同的。该结构还提供了一个几何框架斜$(GL(m), GL(n))$对偶和确定的自然基础的权空间中Nakajima的建设与自然基础的重数空间的张量积，它产生于仿射格拉斯曼。
We give an inductive proof that the generalized Severi varieties -- the varieties which parametrize (irreducible) plane curves of given degree and genus, with a fixed tangency profile to a given line at several general fixed points and several mobile points -- are irreducible.
Smooth quiver quotient varieties
本文对具有半单表示类的光滑空间的箭图及相应的维数向量进行了分类。其结果是，可以通过一些特定的缩减步骤将这些设置缩减为3个简单类型。
Lectures on Nakajima's Quiver Varieties
这是在暑期学校“几何方法在表示论“（格勒诺布尔，2008年）的讲座的扩展版本。
Given a quiver, Nakajima introduced the quiver variety and the Hecke correspondence, which is a closed subvariety of Cartesian products of quiver varieties. In this paper, we consider two nested quiver varieties as fiber products of Hecke correspondences along natural projections. After blowing up the diagonal, we prove that they are isomorphic to a quadruple moduli space which Neguţ observed for the Jordan quiver. The main ingredient is Jiang's derived projectivization theory and Hekking's derived blow-up theory, while we obtain the local model when both the two derived schemes are quasi-smoo…
We investigate the irreducibility of the nilpotent Slodowy slices that appear as the associated variety of W-algebras. Furthermore, we provide new examples of vertex algebras whose associated variety has finitely many symplectic leaves.
Nilpotent quiver varieties with multiplicities and symmetrisable crystals
该研究构造带重数箭图的幂零箭图簇类似物，通过开发新稳定性条件及利用与赫克对应关系的作用，将斋藤对卡茨 - 穆迪代数晶体的几何构造从对称扩展到可对称化情形。
Quiver varieties and Lusztig's algebra
研究了图的预投射代数及其与量子SL（2）表示上模范畴的关系。作为应用，我们证明了Nakajima的ADE簇是由Lusztig引入的某个结合代数的表示簇的子簇.
Hilbert irreducibility for varieties with a nef tangent bundle
本文证明了具有Hilbert型性质的簇的纤维化性质，并将其应用于研究具有nef切丛的簇上的有理点。
Smooth correspondences between quiver varieties
本文提出了一种新的光滑对应于淬火品种，用于构建奇点解析并证明其不可约性和Cohen-Macaulay性质，扩展了之前关于希尔伯特方案的研究。
Arithmetic harmonic analysis on character and quiver varieties II
我们研究了穿孔黎曼曲面基本群的类属特征标簇的拓扑结构、Macdonald多项式、代数表示、曲面上的Hilbert格式、有限一般线性群的不可约特征标的模形式和张量积中的重数之间的联系。
Homological approach to the Hernandez-Leclerc construction and quiver varieties
在以前的论文中，作者已经附加到每个Dynkin的一个结合代数。定义是范畴的，代数用于构造任意非格拉斯曼的去奇异化。在本文中，我们证明了这个代数是同构于一个代数构造的Hernandel-Leclerc定义的组合，并用于描述某些分次Nakajima簇。这种方法是用来得到一个明确的实现的轨道封闭的表示Dynkin箭图作为仿射矢量。
Nakajima quiver varieties in dimension four
本文通过组合方法对四维Nakajima标量簇进行了分类，并反驳了关于G₄商奇异性能否作为quiver簇的疑问。
Quasi-projective varieties are Grassmannians for fully exact subcategories of quiver representations
本文通过限制Reineke同构到完全正合子范畴，证明拟射影簇可表示为箭图格拉斯曼流形。
Quiver varieties and Frenkel-Kac construction
仿射李代数作用在仿射型簇的上同调群上。一个海森堡代数作用在点的Hilbert概型的上同调群上，且作用在Kleinian奇点的极小分解上。我们表明，在类型$A$的情况下，前者是由后者的Frenkel-Kac建设。
Kac's conjecture from Nakajima quiver varieties
证明了Nakajima簇的贝蒂数的生成函数公式。我们证明了它是Weyl-Kac特征标公式的q-变形。特别地，这意味着计数绝对不可分解的表示的个数的多项式的常数项等于相应的Kac-Moody代数中的某个权重的重数，Kac在1982年证明了这一点。
A categorical action on quantized quiver varieties
在本文中，我们描述了任何Kac-Moody代数在Nakajima箭图簇上的量化相干层范畴上的范畴作用。所谓“量子化相干层”，我们指的是一类模层，它是在自然辛结构的变形量子化上的。这个作用是Nakajima的泛包络代数的尺规作图法的直接范畴化。
Vector bundles on projective varieties and representations of quivers
我们提出了某些类别的向量丛的投射品种，即上核束，施泰纳束，合合束，单子，和满子范畴的某些箭图表示之间的等价关系。作为一个应用程序，我们提供了这样的捆绑分解的标准。
Quiver varieties and adjoint crystals of level $\ell$ for type $A_n^{(1)}$
设$B(Λ)$是量子仿射代数$U_q(A_n^{(1)})$的一个水平$\ell$最高权晶体.我们构造了一个明确的晶体同构之间的几何实现$\gB(Λ)$的晶体$B(Λ)$使用的各种和路径实现$\mathcal{P}^{\rm ad}(Λ)$所产生的伴随晶体$\Bad{\ell}$的水平$\ell$。
Schubert Quiver Grassmannians
Quiver Grassmannian是一个射影簇，它在一个实数表示中参数化给定维数的子表示。我们定义了一个类的Grassmannian推广那些实现退化旗品种。我们表明，每一个不可约组件的问题是同构的Schubert品种的Grassmannian。我们给出了一个明确的描述的一组不可约的组件，确定所有的舒伯特品种出现，并计算庞加莱多项式的这些Grassmannian。
Rational smoothness of varieties of representations for quivers of Dynkin type
借助于Lusztig的标准基，我们研究了A、D或E型表示的轨道的Zapriki闭包的局部交上同调。特别地，我们刻画了有理光滑轨道，并证明了轨道闭包是光滑的当且仅当它们是有理光滑的。这提供了V.Deodhar和J.Carrell和D.彼得森对舒伯特品种。
Irreducibility of Newton strata in GU(1,n-1) Shimura varieties
设L是二次虚域，在有理数素数p处不动，设整数n至少为3，M是n维主极化阿贝尔簇的模空间（特征p），其特征为（1，n-1）.我们证明了M的每个牛顿层，除了超奇异层，都是不可约的。
Let $(S,L)$ be a polarized $K3$ surface of genus $p \geqslant 11$ such that $\mathrm{Pic}(S)=\mathbf{Z}[L]$, and $δ$ a non-negative integer. We prove that if $p\geqslant 4δ-3$, then the Severi variety of $δ$-nodal curves in $|L|$ is irreducible.
Topology of character varieties and representations of quivers
在arXiv：0810.2076中，我们提出了一个猜想，推广了Macdonald多项式的Cauchy公式。该猜想将黎曼曲面的表示簇的混合Hodge多项式在其穿孔处用半单共轭类进行编码。我们证明了支持这一猜想的几个结果。在这里，我们宣布了新的结果，这些结果是arXiv：0810.2076的结果。
In the literature there are two ways of endowing an affine ind-variety with a topology. One possibility is due to Shafarevich and the other to Kambayashi. In this paper we specify a large class of affine ind-varieties where these two topologies differ. We give an example of an affine ind-variety that is reducible with respect to Shafarevich's topology, but irreducible with respect to Kambayashi's topology. Moreover, we give a counter-example of a supposed irreducibility criterion of Shafarevich which is different from a counter-example given by Homma. We finish the paper with an irreducibility…
Torus orbits on homogeneous varieties and Kac polynomials of quivers
本文证明了部分旗簇乘积中某些环面轨道的计数多项式与超新星箭图的Kac多项式是一致的，这是在研究射影线上平凡丛上某些非正则亚纯联络的模空间时出现的.我们还证明了这些多项式可以表示为特定图的Tutte多项式的一个特殊化，提供了其系数的非负性的组合证明。
Quiver flag varieties and multigraded linear series
本文引入了一类光滑投射簇，它推广并共享了A型部分旗簇的许多性质。有限非循环群Q（具有唯一源）和维数向量r的旗簇M_ \vartheta（Q，r）是Q的稳定表示的细模空间.箭旗簇是Mori Dream空间，它们通过Grassmann丛的塔得到，它们的相干层的有界导出范畴由倾斜丛生成。本文定义了局部自由层的弱例外序列E =（O_X，E_1，.）的重分次线性级数，E_ρ）是由E编码的对（Q，r）的带标志簇|E| = M_ \vartheta（Q，r）.当每个E_i是全局生成的时，我们获得一个态射_ |E|：X -> |E|，将每个E_i实现为重言式束的拉回。作为应用，我们引入了一个带旗簇的多重Plucker嵌入
For a finite subgroup $Γ\subset \mathrm{SL}(2,\mathbb{C})$ and $n\geq 1$, we construct the (reduced scheme underlying the) Hilbert scheme of $n$ points on the Kleinian singularity $\mathbb{C}^2/Γ$ as a Nakajima quiver variety for the framed McKay quiver of $Γ$, taken at a specific non-generic stability parameter. We deduce that this Hilbert scheme is irreducible (a result previously due to Zheng), normal, and admits a unique symplectic resolution. More generally, we introduce a class of algebras obtained from the preprojective algebra of the framed McKay quiver by a process called cornering, a…
The goal of this paper is to clarify the connection between certain structures from the theory of totally nonnegative Grassmannians, quiver Grassmannians for cyclic quivers and the theory of local models of Shimura varieties. More precisely, we generalize the construction from our previous paper relating the combinatorics and geometry of quiver Grassmanians to that of the totally nonnegative Grassmannians. The varieties we are interested in serve as realizations of local models of Shimura varieties. We exploit quiver representation techniques to study the quiver Grassmannians of interest and, …
The irreducibility of Hurwitz spaces and Severi varieties on toric surfaces
本文通过热带几何方法，证明了在任意代数闭域上经典Hurwitz空间的不可约性，并建立了丰富托里曲面类（包括所有经典托里曲面）上Severi簇在任意特征下的不可约性。
Quiver Varieties with Multiplicities, Weyl Groups of Non-Symmetric Kac-Moody Algebras, and Painlevé Equations
对于每个顶点都有正整数的有限流形，我们给出了一个具有参数的全纯辛流形。这与Nakajima的无稳定性参数/框架（如果附加在顶点上的整数都等于1的话）的numerical簇一致。本文将Kac-Moody代数簇的反射函子的构造推广到我们的情形，其中这些反射函子与可对称化的、可能非对称的Kac-Moody代数的外尔群中的单反射有关.我们把黎曼球面上秩为2的平凡丛上的亚纯联络的模空间描述为流形。在我们的图中，Painlevé方程的Dynkin图列表与Okamoto的略有不同（但等价于）。
On the equations and classification of toric quiver varieties
研究了复曲面的复曲面簇（复曲面表示的模空间）.给定一个顶点和一个权，有一个相关的拟投射复曲面簇连同一个到射影空间的规范嵌入。它表明，对于一个没有定向圈的环的齐次理想，这个嵌入的射影簇是由度至多为$3$的元素生成的。在每个固定维数$d$中，直到同构，只有1000个$d$维复曲面簇。概述了它们的分类程序。
On defining irreducibility
我们证明了不可约性不是实代数簇的一阶可定义性质。证明是基于最近的o-极小结果的指数函数。我们猜想不可约性不是复代数簇的可定义性质。
The $\imath$quiver algebras were introduced recently by the authors to provide a Hall algebra realization of universal $\imath$quantum groups, which is a generalization of Bridgeland's Hall algebra construction for (Drinfeld doubles of) quantum groups; here an $\imath$quantum group and a corresponding Drinfeld-Jimbo quantum group form a quantum symmetric pair. In this paper, the Dynkin $\imath$quiver algebras are shown to arise as new examples of singular Nakajima-Keller-Scherotzke categories. Then we provide a geometric construction of the universal $\imath$quantum groups and their ``dual can…
We give an explicit description of the irreducible components of two-row Springer fibers in type A as closed subvarieties in certain Nakajima quiver varieties in terms of quiver representations. By taking invariants under a variety automorphism, we obtain an explicit algebraic description of the irreducible components of two-row Springer fibers of classical type. As a consequence, we discover relations on isotropic flags that describe the irreducible components.
We present a review on the recently discovered link between the Lie theory,the theory of quiver Grassmannians, and various degenerations of flag varieties. Our starting point is the induced Poincaré--Birkhoff--Witt filtration on the highest weight representations and the corresponding PBW degenerate flag varieties.
Quiver Grassmannians and degenerate flag varieties
Quiver Grassmannian是一个参数化子表示的变种。据观察，A型箭图的某些Grassmannian与第二位作者早先研究的退化旗变种同构。这导致考虑一类Grassmannian的子表示的直和的一个投射和一个内射表示Dynkin的。它被证明是（通常是奇异的）不可约正常的局部完全相交品种，其中承认一个群作用与许多轨道，和细胞分解。对于A型箭图，导出了欧拉示性数（Genocchi数的中值）和Poincare多项式的显式表达式。
Symplectic resolutions of quiver varieties
本文从辛代数几何角度研究中岛箭图簇，证明其均为辛奇点，完整分类了允许辛解消的情形，并推广了Le Bruyn关于光滑轨迹的结果，发现并非所有辛解消都源于GIT变化。
Białynicki-Birula Decompositions of Nakajima Quiver Varieties, Quiver Chains and Star-Shaped Quivers
研究中岛箭图簇相关的比亚林斯基 - 比鲁拉分解，通过箭图链描述不动点，探讨分解几何，如吸引纤维维度等，还将框架用于星形箭图，对特定维数向量分类不动点轨迹分量并计算动机类。
Projective toric varieties as fine moduli spaces of quiver representations
本文证明了每一个投射环面簇都是一个适当有界簇的稳定表示的细模空间。为了实现这一点，我们研究了$Q$与关系$R$对应的有限维代数$\bigl(\bigoplus_{i=0}^{r} L_i \bigr)$，其中$\mathcal{L} := (\mathscr{O}_X,L_1, ...c, L_r)$是一个列表上的线丛的投射环面品种$X$。$Q$定义了一个光滑的投射环面簇，称为多线性级数$|\mathcal{L}|$，以及一个映射$X \to |\mathcal{L}|$。给出了诱导映射为闭嵌入的充要条件。由此得到了投射复曲面簇的一个新的几何商构造。在对$\mathcal{L}$稍强的假设下，封闭嵌入将$X$与用于有界多项式$(Q,R)$的稳定表示的精细模空间识别。
Quiver Grassmannians for the Bott-Samelson resolution of type A Schubert varieties
本文将A型Schubert簇的Bott-Samelson解消实现为箭图Grassmannian，通过引入置换的几何相容分解概念和构造带关系的特殊箭图，显式建立了这两者之间的同构关系。
Quiver grassmannians, quiver varieties and the preprojective algebra
箭图在代数的表示论中起着重要的作用，其关键成分是路代数和预投射代数。箭图Grassmannian是路或预投射代数的固定模的子模的变种。在本文中，我们详细研究了这些对象。我们表明，对应于某些内射模的子模的拉格朗日grassmannian同胚的中岛已被很好地研究了在几何表示论的背景下。然后，我们完善这一结果，找到同胚的Demazure的品种介绍的第一作者，和其他同胚的分级/循环的品种Nakajima。Demazure Grassmannian允许我们在预投射代数的局部幂零模范畴中描述内射对象。最后，我们将我们的结构与Lusztig使用投射词代替内射词的类似结构联系起来。
A Geometric Realization of Spin Representations and Young diagrams from Quiver Varieties
应用技术的早期文件与弗伦克尔，我们开发了一个几何实现的旋量表示和Clifford代数。在这样做时，我们给出了明确的参数化的不可约组件Nakajima品种的D型的杨图。我们显式地计算了该李代数的几何作用量，并将其推广到整个Clifford代数上，用于旋量表示的经典构造.
Quivers variety for affine orthogonal quiver
本文研究正交箭图的箭图簇，利用预投影代数中的图形演算，确定了由仿射Dynkin图产生的Kleinian曲面奇点类型。
Bases of representations of type A affine Lie algebras via quiver varieties and statistical mechanics
我们涉及两个明显不同的基地表示的仿射李代数的A型：一个产生于统计力学，其他从规范理论。我们表明，这两个是由相同的组合，因此可以被视为相同的。特别地，我们能够给出E的一个结果的另一种更简单的几何证明。日期，M。Jimbo，A. Kuniba，T. Miwa和M. Okado关于仿射李代数表示的基的构造。同时，我们给出了一个简单的参数化的Nakajima的不可约组件的各种相关的无限和循环箭图。我们还定义了新的品种，其不可约的组件是在一对一的对应关系与基地的最高权表示的仿射gl_{n+1}。
Seiberg duality conjecture asserts that the Gromov-Witten theories (Gauged Linear Sigma Models) of two quiver varieties related by quiver mutations are equal via variable change. In this work, we prove this conjecture for $A_n$ type quiver varieties.
We review the definition of quiver varieties and their relation to representation theory of Kac-Moody Lie algebras. Target readers are ring and representation theorists. We emphasize important roles of first extension groups of the preprojective algebra associated with a quiver.
Linear degenerate flag varieties are degenerations of flag varieties as quiver Grassmannians. For type A flag varieties, we obtain characterizations of flatness, irreducibility and normality of these degenerations via rank tuples. Some of them are shown to be isomorphic to Schubert varieties and can be realized as highest weight orbits of partially degenerate Lie algebras, generalizing the corresponding results on degenerate flag varieties. To study normality, cell decompositions of quiver Grassmannians are constructed in a wider context of equioriented quivers of type A.
Quiver description of bow varieties in general type
本文为任意类型的 Cherkis bow 簇提供箭图描述，推广 Nakajima 箭图簇构造，并给出稳定性、非空性与光滑性判据。
On the Irreducibility of Commuting Varieties of Nilpotent Matrices
给定一个代数闭域K上的n × n幂零矩阵，证明了与之可交换的所有n × n幂零矩阵的集合的性质，并证明了当char K = 0或char K不小于n/2时，所有n × n幂零矩阵对（A，B）簇的不可约性.作为结果，我们证明了在K上光滑代数曲面的n个点的局部Hilbert格式在上述条件下是不可约的。
We study the algebraic geometry of twisted Higgs bundles of cyclic type along complex curves. These objects, which generalize ordinary cyclic Higgs bundles, can be identified with representations of a cyclic quiver in a twisted category of coherent sheaves. Referring to the Hitchin fibration, we produce a fibre-wise geometric description of the locus of such representations within the ambient twisted Higgs moduli space. When the genus is 0, we produce a concrete geometric identification of the moduli space as a vector bundle over an associated (twisted) A-type quiver variety; we count the numb…
We study smoothness of toric quiver varieties. When a quiver $Q$ is defined with the identity dimension vector, the corresponding quiver variety is also a toric variety. So it has both fan representation and quiver representation. We work only on quivers with canonical weight and we classify smooth such toric quiver varieties. We show that a variety corresponding to a quiver with the identity dimension vector and the canonical weight is smooth if and only if it is a product of projective spaces or their blowups.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。