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1 results

  • Gorenstein rings through face rings of manifolds

  • Part of
  • Isabella Novik, Ed Swartz
  • Journal:
    Compositio Mathematica / Volume 145 / Issue 4 / July 2009
    Published online by Cambridge University Press:
    01 July 2009, pp. 993-1000
    Print publication:
    July 2009
    • Article
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  • 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 g-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.