摘要翻译:
三次四折的周期映射取维数为20的正交类型的局部对称变化的值。我们确定了这个周期映射的映像(从而证实了Hassett的一个猜想),同时给出了Voisin定理的一个新的证明,该定理断言这个周期映射是一个开嵌入。我们的主要结果的一个代数版本是在一个20维正交型对称域上用一个亚纯自守形式的代数在6个复变量的三次型空间上的SL(6)-不变多项式代数的辨识。我们还用Dynkin-Vinberg图描述了半可定三次四折叠模空间的分层。
---
英文标题:
《The period map for cubic fourfolds》
---
作者:
Eduard Looijenga
---
最新提交年份:
2007
---
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
--
---
英文摘要:
The period map for cubic fourfolds takes values in a locally symmetric variety of orthogonal type of dimension 20. We determine the image of this period map (thus confirming a conjecture of Hassett) and give at the same time a new proof of the theorem of Voisin that asserts that this period map is an open embedding. An algebraic version of our main result is an identification of the algebra of SL(6)-invariant polynomials on the space of cubic forms in 6 complex variables with a certain algebra of meromorphic automorphic forms on a symmetric domain of orthogonal type of dimension 20. We also describe the stratification of the moduli space of semistable cubic fourfolds in terms of a Dynkin-Vinberg diagram.
---
PDF链接:
https://arxiv.org/pdf/0705.0951