摘要翻译:
设$x_1,...,x_m$表示特征为0的代数闭域上的属$g_i\geq2$的光滑射影曲线,设$n$表示至少等于$1+\max_{i=1}^m g_i$的任意整数。我们证明了相应的Jacobian变体的乘积$jx_1\乘以...\乘以Jx_m$具有指数$n^{m-1}$的Prym-Tyurin变体的结构。这个指数比Prym-Tyurin变种的结构指数要小得多,而Prym-Tyurin变种已知存在于任意主极化阿贝尔变种中。此外,它是由显式对应关系给出的。
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英文标题:
《Products of Jacobians as Prym-Tyurin varieties》
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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 $X_1, ..., X_m$ denote smooth projective curves of genus $g_i \geq 2$ over an algebraically closed field of characteristic 0 and let $n$ denote any integer at least equal to $1+\max_{i=1}^m g_i$. We show that the product $JX_1 \times ... \times JX_m$ of the corresponding Jacobian varieties admits the structure of a Prym-Tyurin variety of exponent $n^{m-1}$. This exponent is considerably smaller than the exponent of the structure of a Prym-Tyurin variety known to exist for an arbitrary principally polarized abelian variety. Moreover it is given by explicit correspondences.
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PDF链接:
https://arxiv.org/pdf/0805.4785