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Gorenstein rings through face rings of manifolds
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Description
<jats:title>Abstract</jats:title><jats:p>The face ring of a homology manifold (without boundary) modulo a generic system of parameters is studied. Its socle is computed and it is verified that a particular quotient of this ring is Gorenstein. This fact is used to prove that the algebraic <jats:italic>g</jats:italic>-conjecture for spheres implies all enumerative consequences of its far-reaching generalization (due to Kalai) to manifolds. A special case of Kalai’s conjecture is established for homology manifolds that have a codimension-two face whose link contains many vertices.</jats:p>
Journal
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- Compositio Mathematica
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Compositio Mathematica 145 (4), 993-1000, 2009-07
Wiley
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Details 詳細情報について
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- CRID
- 1360855569096000768
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- ISSN
- 15705846
- 0010437X
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- Data Source
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- Crossref