摘要翻译:
给出了复射影空间P^n上光滑Weierstrass曲线模栈的基本群的有限表示,将椭圆曲线的经典结果推广到正维基。由此我们得到了SL_2(Z)的自然推广,并为一般理解椭圆曲面模叠的基本群铺平了道路。我们的方法利用Weierstrass曲线上的自然对合和它的固定轨迹与光滑超曲面在适当的线性方程组中的识别。相应的判别补的基本群可以用Zariski传统方法的有限个生成元和关系表示,这些方法在Mathag/0602371中得到了详细的阐述。
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英文标题:
《Fundamental groups of moduli stacks of smooth Weierstrass fibrations》
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作者:
Michael L\"onne
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最新提交年份:
2007
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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 give finite presentations for the fundamental group of moduli stacks of smooth Weierstrass curves over complex projective space P^n which extend the classical result for elliptic curves to positive dimensional base. We thus get natural generalisations of SL_2(Z) and pave the way to understanding the fundamental group of moduli stacks of elliptic surfaces in general. Our approach exploits the natural involution on Weierstrass curves and the identification of its fixed loci with smooth hypersurfaces in an appropriate linear system on a projective line bundle over P^n. The fundamental group of the corresponding discriminant complement can be presented in terms of finitely many generators and relations using methods in the Zariski tradition, which were sucessfully elaborated in mathAG/0602371.
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PDF链接:
https://arxiv.org/pdf/0712.3374