Simplicity of generic Steiner bundles
Maria Chiara Brambilla
证明了一般Steiner丛E是单的当且仅当E的自同态丛的欧拉示性数小于等于1。特别是，我们证明了E是例外的，或者它满足以下不等式t \leq（\frac{n+1+\sqrt((n+1)^2-4)}{2}）s。
We prove that a generic Steiner bundle E is simple if and only if the Euler characteristic of the endomorphism bundle of E is less or equal to 1. In particular we show that either E is exceptional or it satisfies the following inequality t\leq(\frac{n+1+\sqrt((n+1)^2-4)}{2})s.
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
Jumping pairs of Steiner bundles
本文引入了Grassmannian上Schwarzenberger丛的定义。回顾Steiner丛的概念，我们推广了Grassmannian上Steiner丛的跳对概念。在研究了跳跃轨迹簇及其维数界之后，给出了具有最大维数跳跃轨迹的Steiner丛的完全分类，它们都是Schwarzenberger丛。
Linear and Steiner bundles on projective varieties
利用算术Cohen-Macaulay（ACM）簇的Horrocks单子的推广，建立了射影空间和二次超曲面上线性丛和Steiner丛的上同调刻画.我们还研究了ACM簇上丛的线丛分解，并在二次超曲面的情况下刻画了线性同调维数。
In this work we study $k$-type uniform Steiner bundles, being $k$ the lowest degree of the splitting. We prove sharp upper and lower bounds for the rank in the case $k=1$ and moreover we give families of examples for every allowed possible rank and explain which relation exists between the families. After dealing with the case $k$ in general, we conjecture that every $k$-type uniform Steiner bundle is obtained through the proposed construction technique.
Restrictions of Steiner bundles and divisors on the Hilbert scheme of points in the plane
射影平面中n个点的Hilbert方案参数化了射影平面的n次零维子方案。我们研究了Hilbert格式上有效因子和移动曲线的对偶锥。通过研究插值，限制，和稳定性的某些向量丛在平面上，我们完全确定这些锥刚刚超过四分之三的所有值的n。P^N上的一般Steiner丛是允许特定形式的线性分解的向量丛。证明了P^N上的半稳定Steiner丛的每一个容许斜率都是由一个约束于有理曲线上的半稳定丛的丛实现的，从而完成了P^N上半稳定Steiner丛的斜率的分类.这个证明涉及到一个关于P^1上多项式乘法的基本问题，这个问题本身就很有趣。
A Steiner bundle is a vector bundle on projective space arising as the cokernel of the map defined by a matrix of linear forms. These come up in various geometric settings, and by now they are the subject of a considerable literature. Starting with work of Dolgachev and Kapranov from 1993, several authors have considered the question of whether one can recover from the bundle the geometric data used to construct it. Here we prove such Torelli-type statements for the tautological bundles associated to sufficiently positive divisors on any very ample linear series. In an appendix, we give a new …
Le probleme de Brill-Noether pour les fibre's de Steiner et application aux courbes gauches
3-射影空间上的Steiner丛是由线性型矩阵定义的态射的平凡丛的核。我们构造了各种秩为n的Steiner丛E，使得E（1）有n-1个截面，其依赖轨迹是一条平滑曲线.
Unstable hyperplanes for Steiner bundles and multidimensional matrices
本文研究了$SL(V_0) \times...\times SL(V_p)$对非退化多维复矩阵$A\in¶(V_0\otimes...\otimes V_p)$的边界形式（在Gelfand，Kapranov和Zelevinsky的意义下）的自然作用的一些性质，特别地，我们把非稳定的矩阵刻画为在“三角形”矩阵的轨道上的矩阵，把含有$\C^*$的稳定子的矩阵刻画为在“对角”矩阵的轨道上的矩阵.对于$p=2$，证明了非退化矩阵$A\in¶(V_0\otimes V_1\otimes V_2)$在射影空间$¶^{n}, n = dim (V_2)-1$上检测Steiner丛$S_A$（在Dolgachev和Kapranov的意义下）。由此证明了Steiner丛的对称群包含在SL（2）中，SL（2）不变Steiner丛正是Schwarzenberger [Schw]引入的对应于“单位”矩阵的丛.我们可以刻画Steiner丛的模空间中对于$Aut(¶^n)$的作用是稳定的点，在第一个非平凡的情况下回答了Simpson提出的一个问题。在相反的方向上，我们得到了一些结果的Steiner丛，其中包含性质的矩阵。例如，$S_A$的不稳定超平面的数量（计算多重性）产生了$A$的一个有趣的离散不变量，它可以取值为$0, 1, 2, ... ,\dim~V_0+1$或$ \infty$ ; $\infty$…
Stabilizers for nondegenerate matrices of boundary format and Steiner bundles
本文利用射影空间上的Steiner向量丛与$V_0 \otimes ... \otimes V_p$中边界格式的非退化多维矩阵的联系，研究了它们的性质.对于任何非退化矩阵$A$的稳定剂的$SL(V_0)\times ... \times SL(V_p)$ -行动，$Stab(A)$，是完全描述。特别地，我们证明了SL（2）在$V_0 \otimes ... \otimes V_p$上存在一个显式作用，使得$Stab(A)^0\subseteq SL(2)$和等式成立当且仅当$A$属于包含单位矩阵的唯一$SL(V_0)\times >... \times SL(V_p)$ -轨道.
Schwarzenberger bundles on smooth projective varieties
定义了任意光滑射影簇X上的Schwarzenberger丛。本文引入了Steiner丛E在X上的跳跃对的概念，并确定了其跳跃轨迹维数的一个界。对跳对集具有最大维数的Steiner丛进行了完全分类，证明了它们都是Schwarzenberger丛。
Uniform Steiner bundles on $\mathbb{P}^n$ and reflection functors
该研究证明了$n\geq2$时$\mathbb{P}^n$上存在$k\geq4$型的一致非齐次Steiner丛（分裂型不连通），还研究了近一致Steiner丛，方法是将Steiner丛视为相对射影Kronecker表示并应用限制、膨胀与反射函子的伴随对。
Simplicity and exceptionality of syzygy bundles over P^n
在这项工作中，我们将证明的结果，确保简单性和特殊性的向量丛，这是由分裂的纯决议。我们称这样的物体为合朔丛。
Schwarzenberger bundles of arbitary rank on the projective space
在射影空间上引入了Schwarzenberger丛的一个推广概念。与这个更一般的定义相关联，我们给出了${\Bbb P^n}$上Steiner丛的跳跃子空间的一个特别概念（在秩$n$上与Vallès，Ancona和Ottaviani引入的不稳定超平面的概念相一致）。对于跳跃超平面的集合，我们找到了它的维数的一个精确界。对跳跃超平面集具有最大维数的Steiner丛进行了分类，并证明了它们是广义Schwarzenberger丛。
Representations of Kronecker quivers and Steiner bundles on Grassmannians
本文利用Auslander-Reiten理论和反射函子研究Grassmann流形上Steiner丛与广义Kronecker箭图相对投射表示满子范畴之间的对应关系，并开创了对野表示范畴中与初等测试模右Hom-正交的满子范畴的研究。
The variety of minimal rational tangents associated to Hecke curves was used by J.-M.Hwang [8] to prove the simplicity of the tangent bundle on the moduli of vector bundles over a curve. In this paper, we use the tangent maps of the symplectic and orthogonal Hecke curves to prove an analogous result for symplectic and orthogonal bundles. In particular, we show the nondegeneracy of the associated variety of minimal rational tangents, which implies the simplicity of the tangent bundle on the moduli spaces of symplectic and orthogonal bundles over a curve. We also show that for large enough genus…
In this paper, we study the cohomology of vector bundles on projective space defined as kernels or cokernels of general maps $V_1 \to V_2$, where the $V_i$ are direct sums of line bundles or certain exceptional bundles. We prove an asymptotic cohomology vanishing theorem. We characterize the stability of general Steiner bundles on projective space. We also give a criterion for a Steiner bundle to be ample.
The Simplicity of the Hodge Bundle
本文证明了亏格 $g \geq 2$ 的曲线模空间上的 Hodge 丛不包含任何非平凡子丛。
Recently, Kanemitsu has discovered a counterexample to the long-standing conjecture that the tangent bundle of a Fano manifold of Picard number one is (semi)stable. His counterexample is a smooth horospherical variety. There is a weaker conjecture that the tangent bundle of a Fano manifold of Picard number one is simple. We prove that this weaker conjecture is valid for smooth horospherical varieties of Picard number one. Our proof follows from the existence of an irreducible family of unbendable rational curves whose tangent vectors span the tangent spaces of the horospherical variety at gene…
Invariant multidimensional matrices
如果$¶^n$上的秩$n$ Steiner丛是$SL(2,\C)$不变的，则它是Schwarzenberger丛
On simplicity and stability of tangent bundles of rational homogeneous varieties
给定一个有理齐次簇G/P，其中G是ADE型复单簇，我们证明了所有的切丛T_{G/P}都是单簇，这意味着它们唯一的自同态是单位元的标量倍数.这个结果与Hitchin-Kobayashi对应相结合，暗示了这些切丛关于反正则极化的稳定性。我们的主要工具是G/P上的齐次向量丛与具有关系的有限维表示之间范畴的等价性。
We consider the question of simplicity of a ring $R$ under the action of its ring of differential operators $D_R$. We give examples to show that even when $R$ is Gorenstein and has rational singularities $R$ need not be a simple $D_R$-module; for example, this is the case when $R$ is the homogeneous coordinate ring of a smooth cubic surface. Our examples are homogeneous coordinate rings of smooth Fano varieties, and our proof proceeds by showing that the tangent bundle of such a variety need not be big. We also give a partial converse showing that when $R$ is the homogeneous coordinate ring of…
Steiner representations of hypersurfaces
本文证明超曲面上的局部Cohen-Macaulay instanton层可诱导射影空间上同秩Steiner丛之间的态射，使定义超曲面的形式的幂等于该态射的行列式，并给出低次数情形及光滑整曲面的pfaffian表示。
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。