摘要翻译:
在七维三次球谐空间上定义了一个六次不变量J,并证明了J是正的当且仅当球谐的结点集正好包含两个正二十面体的顶点。利用Clebsch对角三次曲面的几何学、Atiyah对椭圆曲线上向量丛的分类和Mukai提出的Fano三重法进行证明。
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英文标题:
《Spherical harmonics and the icosahedron》
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作者:
Nigel Hitchin
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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 define a sextic invariant J on the seven-dimensional space of degree three spherical harmonics and show that J is positive if and only if the nodal set of the spherical harmonic contains the vertices of exactly two regular icosahedra. The proof uses the geometry of the Clebsch diagonal cubic surface, Atiyah's classification of vector bundles on an elliptic curve and a Fano threefold introduced by Mukai.
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PDF链接:
https://arxiv.org/pdf/0706.0088