发帖
雷达卡
摘要翻译：
证明了$\mathbb{CP}^n$中齐次簇的一个一般的外在刚性定理。利用该定理证明了复单李代数$\mathfrak{g}$的伴随簇($\mathbb{P}\mathfrak{g}$中唯一的极小g轨道）外刚性到三阶。与此相反，我们证明了伴随变种$sl_3\mathbb{C}$和Segre积$\mathit{Seg}(\mathbb{P}^1\times\mathbb{P}^n)$,这两个具有密切序列长度为2的变种在二阶上是灵活的。在$SL_3\MathBB{C}$例子中，我们讨论了外射影几何与内路径几何之间的关系。我们将Hwang和Yamaguchi、Se-ashi、Tanaka等人所发展的机械学推广到将一般定理的证明归结为李代数上同调计算。柔度陈述的证明采用外微分系统技术。
---
英文标题：
《Fubini-Griffiths-Harris rigidity and Lie algebra cohomology》
---
作者：
J.M. Landsberg and C. Robles
---
最新提交年份：
2008
---
分类信息：
一级分类：Mathematics 数学
二级分类：Differential Geometry 微分几何
分类描述：Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
复形，接触，黎曼，伪黎曼和Finsler几何，相对论，规范理论，整体分析
--
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--
一级分类：Mathematics 数学
二级分类：Representation Theory 表象理论
分类描述：Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示，李理论，结合代数，多重线性代数
--
---
英文摘要：
We prove a general extrinsic rigidity theorem for homogeneous varieties in $\mathbb{CP}^N$. The theorem is used to show that the adjoint variety of a complex simple Lie algebra $\mathfrak{g}$ (the unique minimal G orbit in $\mathbb{P}\mathfrak{g}$) is extrinsically rigid to third order. In contrast, we show that the adjoint variety of $SL_3\mathbb{C}$, and the Segre product $\mathit{Seg}(\mathbb{P}^1\times \mathbb{P}^n)$, both varieties with osculating sequences of length two, are flexible at order two. In the $SL_3\mathbb{C}$ example we discuss the relationship between the extrinsic projective geometry and the intrinsic path geometry. We extend machinery developed by Hwang and Yamaguchi, Se-ashi, Tanaka and others to reduce the proof of the general theorem to a Lie algebra cohomology calculation. The proofs of the flexibility statements use exterior differential systems techniques.
---
PDF链接：
https://arxiv.org/pdf/0707.3410
京公网安备 11010802022788号
