摘要翻译:
我们描述了不可约代数么半群M$在幂等元E$上的局部结构。当$E$为极小值时,我们证明了$M$是核$MEM$(一个齐次空间)上的一个诱导簇,它具有双侧稳定器$M_E$(一个具有零元和稠密单位群的连通仿射半群)。这就得到了当$M$是正规时幂等的稳定器和中心化器的不可约性,以及任意$M$的正规性和光滑性的判据。此外,我们还证明了$M$是Abel簇上的诱导簇,其中光纤是具有稠密单位群的连通仿射半群。
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英文标题:
《Local structure of algebraic monoids》
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作者:
Michel Brion
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最新提交年份:
2008
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分类信息:
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
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英文摘要:
We describe the local structure of an irreducible algebraic monoid $M$ at an idempotent element $e$. When $e$ is minimal, we show that $M$ is an induced variety over the kernel $MeM$ (a homogeneous space) with fibre the two-sided stabilizer $M_e$ (a connected affine monoid having a zero element and a dense unit group). This yields the irreducibility of stabilizers and centralizers of idempotents when $M$ is normal, and criteria for normality and smoothness of an arbitrary $M$. Also, we show that $M$ is an induced variety over an abelian variety, with fiber a connected affine monoid having a dense unit group.
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PDF链接:
https://arxiv.org/pdf/0709.1255