摘要翻译:
我们证明了Cremona变换对二次曲面实点的作用表现出球面、环面和所有不可定向曲面的微分同态的全部复杂性。主要结果表明:如果X是有理的,那么代数自同构群Aut(X)在X的自差同构群Diff(X)中是稠密的。
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英文标题:
《Cremona transformations and diffeomorphisms of surfaces》
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作者:
J\'anos Koll\'ar, Fr\'ed\'eric Mangolte (LM-Savoie)
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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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一级分类:Mathematics 数学
二级分类:Geometric Topology 几何拓扑
分类描述:Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
流形,轨道,多面体,细胞复合体,叶状,几何结构
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英文摘要:
We show that the action of Cremona transformations on the real points of quadrics exhibits the full complexity of the diffeomorphisms of the sphere, the torus, and of all non-orientable surfaces. The main result says that if X is rational, then Aut(X), the group of algebraic automorphisms, is dense in Diff(X), the group of self-diffeomorphisms of X.
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PDF链接:
https://arxiv.org/pdf/0809.3720