摘要翻译:
本文研究了具有极大秩Picard格的K3曲面族的一些例子。这些族作为有限自同构群的不变量出现。考虑了描述这些族中Hodge结构变化的Picard-Fuchs微分方程。发展了寻找相应的单群群作为作用于族周期空间的算术Fuchsian群的技术。
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英文标题:
《Picard-Fuchs Differential Equations for Families of K3 Surfaces》
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作者:
James P Smith
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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:
This thesis studies some examples of families of K3 surfaces with Picard lattices of maximal rank. These families occur as invariants of finite automorphism groups. The Picard-Fuchs differential equations describing the variation of Hodge structure in these families are considered. Techniques are developed to find the corresponding monodromy groups as arithmetic Fuchsian groups acting on the families' period spaces.
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PDF链接:
https://arxiv.org/pdf/0705.3658