Closed manifolds coming from Artinian complete intersections

Ştefan Papadima; Laurenţiu Păunescu

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Closed manifolds coming from Artinian complete intersections

Ştefan Papadima·Laurenţiu Păunescu

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Abstract

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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Ştefan Papadima, Laurenţiu Păunescu. 2004-06-09. Closed manifolds coming from Artinian complete intersections. https://arxiv.org/abs/math/0406161

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