由Artinian完全交生成的闭流形
Closed manifolds coming from Artinian complete intersections
摘要：
本文用经典的判别式和局部不变量重新表述了任意Poincaré $\Q$ -代数的Poincaré内积在中维上的完整性.当代数是1-连通的，我们表明，这个属性是唯一的障碍，实现它的闭流形，到11维。本文重新解释了Eisenbud和Levine关于有限映射芽的一个结果，将映射芽的度与相应局部环的签名联系起来，回答了Halperin关于Artin加权完全交的一个问题，并分析了由4维和8维闭流形实现的$\Q$上的齐次Artin完全交及其签名.
英文摘要：
We reformulate the integrality property of the Poincaré inner product in the middle dimension, for an arbitrary Poincaré $\Q$-algebra, in classical terms (discriminant and local invariants). When the algebra is 1-connected, we show that this property is the only obstruction to realizing it by a closed manifold, up to dimension 11. We reinterpret a result of Eisenbud and Levine on finite map germs, relating the degree of the map germ to the signature of the associated local ring, to answer a question of Halperin on artinian weighted complete intersections.We analyse the homogeneous artinian complete intersections over $\Q$ realized by closed manifolds of dimensions 4 and 8, and their signatures.
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