摘要翻译:
设$G$表示有限群,$\pi:Z\to Y$a光滑射影曲线的Galois覆盖。对于$G$的每个子群$H$,对应的Hecke代数$\MathBB{Q}[H\反斜杠G/H]$在曲线$x=z/H$的雅可比上有一个规范作用。对于$G$的每一个有理不可约表示$\mathcal{W}$,我们将Hecke代数中的一个幂等元联系起来,它导出曲线$x$的对应关系,从而导出雅可比$jx$的一个阿贝尔子簇$p$。我们给出了$\Mathcal{W}$,$H$和$G$对$Z$的作用的充分条件,这些条件表明$P$是Prym-Tyurin变体。通过这种方法,我们得到了许多新的任意指数的Prym-Tyurin变体族。
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英文标题:
《Prym-Tyurin varieties via Hecke algebras》
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作者:
A. Carocca, H. Lange, R. E. Rodriguez and A. M. Rojas
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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:
Let $G$ denote a finite group and $\pi: Z \to Y$ a Galois covering of smooth projective curves with Galois group $G$. For every subgroup $H$ of $G$ there is a canonical action of the corresponding Hecke algebra $\mathbb{Q}[H \backslash G/H]$ on the Jacobian of the curve $X = Z/H$. To each rational irreducible representation $\mathcal{W}$ of $G$ we associate an idempotent in the Hecke algebra, which induces a correspondence of the curve $X$ and thus an abelian subvariety $P$ of the Jacobian $JX$. We give sufficient conditions on $\mathcal{W}$, $H$, and the action of $G$ on $Z$, which imply $P$ to be a Prym-Tyurin variety. We obtain many new families of Prym-Tyurin varieties of arbitrary exponent in this way.
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PDF链接:
https://arxiv.org/pdf/0805.4563